Gr 10 Math Ch 5 SUM: Functions

What does the parameter 'm' represent in the equation of a straight line?

The slope of the graph (correct)

The constant value of c

The x-intercept

The y-intercept

How does the value of 'c' affect the graph of the linear function?

It shifts the graph horizontally.

It affects where the graph cuts the y-axis. (correct)

It has no effect on the graph.

It determines the slope of the line.

If the value of 'm' is negative, which of the following is true about the graph?

The graph slopes downwards from left to right. (correct)

The graph is horizontal.

The graph slopes upwards from left to right.

The graph cannot have a negative slope.

What values can the range of the function f(x) = mx + c take?

Any real number Signup and view all the answers

If 'c' is greater than zero, how does it affect the position of the graph?

The graph shifts vertically upwards. Signup and view all the answers

What is the equation used to calculate the x-intercept of a linear function?

Let y = 0 Signup and view all the answers

Which statement accurately describes the domain of the function f(x) = mx + c?

The domain consists of all real numbers. Signup and view all the answers

In the context of straight-line functions, what happens when 'm' equals zero?

The line is horizontal. Signup and view all the answers

What characterizes the graph of the function when the value of b is greater than 1?

It represents exponential growth. Signup and view all the answers

In the function of the form $y = a an \theta + q$, how does the value of a affect the graph?

It changes the steepness of the graph branches. Signup and view all the answers

Which point is identified as the minimum turning point in the sine function?

(270°, -1) Signup and view all the answers

What is the range of the function $y = a ext{sin} \theta + q$ when $a > 0$?

[q - |a|, q + |a|] Signup and view all the answers

Which of the following statements about the cosine function is true?

The graph has a maximum turning point at (360°, 1). Signup and view all the answers

What is the primary effect of the parameter q in the function $y = a ext{cos} \theta + q$?

It results in a vertical shift of the graph. Signup and view all the answers

What is the period of the tangent function $y = a an \theta + q$?

180° Signup and view all the answers

In the function $y = ab^x + q$, what does the sign of a determine?

If the graph curves upwards or downwards. Signup and view all the answers

What is the domain of the hyperbolic function of the form $y = \frac{a}{x} + q$?

{x : x \in \mathbb{R}, x \neq 0} Signup and view all the answers

Where are the asymptotes for the function $y = an \theta$ located?

At 90° and 270°. Signup and view all the answers

If $a < 0$ in a hyperbolic function, in which quadrants does the graph lie?

Second and fourth quadrants Signup and view all the answers

What happens to the graph of an exponential function when $q < 0$?

The graph shifts vertically downwards by $q$ units Signup and view all the answers

Which type of asymptote is found in the hyperbolic function $y = \frac{a}{x} + q$?

Both vertical and horizontal asymptotes Signup and view all the answers

For the exponential function $y = ab^x + q$, if $a > 0$ and $b > 1$, what can be said about the behavior of the graph?

The graph curves upwards Signup and view all the answers

What do you need to determine first when sketching the graph of the form $y = mx + c$?

sign of m Signup and view all the answers

What characteristic feature is associated with the y-intercept of the hyperbolic function $y = \frac{a}{x} + q$?

It does not exist Signup and view all the answers

In the equation $y = ax^2 + q$, what does the parameter $q$ represent?

The vertical shift of the graph Signup and view all the answers

How is the horizontal asymptote of an exponential function described?

At $y = q$ Signup and view all the answers

How does the gradient $m$ affect the graph of $y = mx + c$?

It measures the relationship between x and y. Signup and view all the answers

What does the variable $q$ represent in the context of hyperbolic functions?

A horizontal asymptote and a vertical shift Signup and view all the answers

What happens to the parabola when $a < 0$ in the equation $y = ax^2 + q$?

It has a maximum turning point. Signup and view all the answers

In which case does the graph of a hyperbolic function intersect the x-axis?

When $y = 0$ Signup and view all the answers

If $a = 2$ in the function $y = ax^2 + q$, which statement is true regarding the shape of the parabola?

It is narrower than when $a = 1$. Signup and view all the answers

What feature distinguishes the axes of symmetry of hyperbolic functions?

They include $y = x + q$ and $y = -x + q$ Signup and view all the answers

What is the range of the function $y = ax^2 + q$ when $a > 0$?

[q; ∞) Signup and view all the answers

To find the x-intercept of a parabola described by $y = ax^2 + q$, you need to:

Set y = 0. Signup and view all the answers

What is the axiom of symmetry for parabolas represented by $f(x) = ax^2 + q$?

It is the line $x = 0$. Signup and view all the answers

If $q < 0$ in the equation $y = ax^2 + q$, what does this indicate about the graph?

The graph is at or below the x-axis. Signup and view all the answers

What does the coefficient $ a $ in the equation of a parabola determine?

The direction and width of the parabola Signup and view all the answers

How can you determine the value of $ q $ for a hyperbola given its equation?

By observing the vertical shift in its graph Signup and view all the answers

To find the points of intersection between two graphs, what mathematical method should be applied?

Equating their expressions Signup and view all the answers

In the equation of sine and cosine functions, how does the value of $ a $ affect the graph?

It affects the amplitude and reflection Signup and view all the answers

What is the primary method for calculating the y-intercept of a graph?

Setting $ x = 0 $ Signup and view all the answers

Which of the following statements about the equation of a hyperbola is true?

$ a $ influences the direction and shape of the hyperbola Signup and view all the answers

What role do asymptotes play in hyperbolas?

They indicate where the function becomes undefined Signup and view all the answers

What does the distance formula primarily calculate between two points?

The straight line distance between the points Signup and view all the answers

Which step is NOT involved when solving for $ a $ and $ q $ from given points in a trigonometric function?

Finding the x-intercept Signup and view all the answers

What effect does the parameter 'b' have in the function of the form $y = ab^x + q$ when $b > 1$?

The function represents exponential growth. Signup and view all the answers

In a sine function described by $y = a ext{sin} heta + q$, what is the effect of $q$ when $q < 0$?

The graph shifts down by $|q|$ units. Signup and view all the answers

What happens to the period of the cosine function when represented in the form $y = rac{1}{2} ext{cos} heta + 1$?

The period remains at 360°. Signup and view all the answers

What is indicated by the x-intercepts of the function $y = an heta$?

The x-intercepts occur at every integer multiple of 180°. Signup and view all the answers

For the function $y = a ext{cos} heta + q$, what is the condition for vertical compression?

|a| < 1. Signup and view all the answers

Which of the following describes the maximum turning point of the sine function $y = ext{sin} heta$?

Occurs at (90°, 1) Signup and view all the answers

What is the primary characteristic of the tangent function's graph?

It has vertical asymptotes at 90° and 270°. Signup and view all the answers

What does the parameter 'a' influence in the function form $y = a ext{tan} heta + q$?

It affects the steepness of the branches. Signup and view all the answers

How does the sign of 'a' in the equation $y = ax^2 + q$ affect the parabola's orientation?

It determines if the parabola opens upwards or downwards. Signup and view all the answers

What describes the domain of the hyperbolic function of the form $y = \frac{a}{x} + q$?

All real numbers except zero Signup and view all the answers

Which of the following correctly describes the y-intercept of the hyperbolic function $y = \frac{a}{x} + q$?

It does not exist Signup and view all the answers

What is the effect of the parameter 'm' when it is equal to zero in the function y = mx + c?

The graph will be a horizontal line. Signup and view all the answers

If $a > 0$ in the exponential function $y = ab^x + q$, what can be inferred about the graph's behavior?

The graph will curve upwards. Signup and view all the answers

What is the effect of changing the value of $q$ in the hyperbolic function $y = \frac{a}{x} + q$?

It shifts the graph vertically. Signup and view all the answers

How does the y-intercept behave when 'c' is less than zero in the equation y = mx + c?

The graph shifts vertically downwards. Signup and view all the answers

When the value of 'm' is positive, what can be said about the direction of the graph?

The graph slopes upwards from left to right. Signup and view all the answers

What characteristic feature distinguishes the range of the hyperbolic function $y = \frac{a}{x} + q$?

It is undefined for values equal to $q$. Signup and view all the answers

Considering the characteristics of the function f(x) = mx + c, what does the domain represent?

All real numbers for x. Signup and view all the answers

Which of the following statements is true regarding the asymptotes of the hyperbolic function?

The horizontal asymptote is at $y = q$. Signup and view all the answers

If $a < 0$ in the hyperbolic function $y = \frac{a}{x} + q$, in which quadrants will the graph primarily lie?

Second and fourth quadrants Signup and view all the answers

What happens to the line represented by y = mx + c if the value of 'm' decreases from a positive to a negative value?

The slope changes from upward to downward. Signup and view all the answers

What is the x-intercept of the hyperbolic function $y = \frac{a}{x} + q$?

Calculated by setting y to 0. Signup and view all the answers

If c = 0 in the equation y = mx + c, what can be inferred about the graph?

The graph is the x-axis. Signup and view all the answers

What is true about the x-intercept of the function y = mx + c?

It is calculated by letting y = 0. Signup and view all the answers

For exponential functions with the form $y = ab^x + q$, when $q < 0$, how is the graph's horizontal asymptote affected?

It shifts vertically downward. Signup and view all the answers

Which axis serves as the line of symmetry for the hyperbolic function $y = \frac{a}{x} + q$?

Line $x = 0$ Signup and view all the answers

What effect does a larger value of 'm' have on the gradient of the linear function?

The gradient increases. Signup and view all the answers

How can the x-intercept of the function in the form $y = ax^2 + q$ be calculated?

Set $y = 0$ and solve for $x$ Signup and view all the answers

What happens to the graph when $a < 0$ in the equation $y = ax^2 + q$?

The graph opens downwards Signup and view all the answers

If the y-intercept $c$ in the equation $y = mx + c$ is greater than zero, where does the graph intersect the y-axis?

At point $(0, c)$ in the first quadrant Signup and view all the answers

What characteristic describes the axis of symmetry in parabolic graphs of the form $y = ax^2 + q$?

It is always the line $x = 0$ Signup and view all the answers

What is the effect of the parameter $q$ in the quadratic function $y = ax^2 + q$?

It shifts the graph vertically up or down Signup and view all the answers

What indicates whether the graph of $y = ax^2 + q$ has a minimum or maximum turning point?

The sign of $a$ Signup and view all the answers

In the gradient and y-intercept method for sketching $y = mx + c$, what do you calculate first?

The y-intercept $c$ Signup and view all the answers

When $0 < a < 1$ in the quadratic function $y = ax^2 + q$, what is the property of the corresponding graph?

The graph widens as $a$ approaches 0 Signup and view all the answers

What describes the domain of the function $y = ax^2 + q$?

It includes all real numbers Signup and view all the answers

How does the gradient $m$ in the linear function $y = mx + c$ impact the graph?

It affects the direction and steepness of the line Signup and view all the answers

How can one determine the sign of parameter 'a' in the equation of a parabola?

By identifying the direction of the parabola Signup and view all the answers

What does the parameter 'q' represent in the context of parabolic equations?

The vertical shift of the parabola Signup and view all the answers

To solve for 'a' and 'q' in a hyperbola using given points, which method should be used?

Substitute the given points into the equations Signup and view all the answers

What is the first step taken when interpreting the graph of a trigonometric function?

Identify the type of trigonometric graph Signup and view all the answers

When finding points of intersection between two graphs, what is the essential step?

Equate the expressions of the two graphs Signup and view all the answers

In the context of graphing parabolas, how do you calculate the y-intercept?

By setting $x$ equal to 0 Signup and view all the answers

In a trigonometric function, how does the value of 'a' affect the graph?

It influences the amplitude and reflection Signup and view all the answers

For the equation of a hyperbola, what role does 'q' play?

Affects the vertical alignment of the graph Signup and view all the answers

Which method is NOT typically involved when solving for 'a' and 'q' from given points in a function?

Calculating the slopes of the given points Signup and view all the answers

What is the significance of identifying asymptotes in graphing hyperbolas?

They help in finding the domain and range Signup and view all the answers

What happens to the slope of the graph when the value of m is negative?

The graph slopes downwards from left to right. Signup and view all the answers

If c = 0 in the equation y = mx + c, where does the graph intersect the y-axis?

At the origin. Signup and view all the answers

How does an increase in the value of c affect the graph of y = mx + c?

It shifts the graph upwards. Signup and view all the answers

What can be said about the domain of the function f(x) = mx + c?

It consists of all real numbers. Signup and view all the answers

In the equation y = mx + c, what occurs when m = 0?

The graph is a horizontal line at y = c. Signup and view all the answers

What describes the behavior of a linear function's x-intercept?

To find it, set y = 0 and solve for x. Signup and view all the answers

What effect does increasing the value of m have on the graph of the linear function?

It steepens the slope of the graph. Signup and view all the answers

If both m and c are negative, how does the graph behave?

The graph slopes downward and intersects the y-axis below zero. Signup and view all the answers

What represents exponential decay in the function of the form $y = ab^x + q$?

$0 Signup and view all the answers

Which point is identified as a minimum turning point for the sine function?

$(270°, -1)$ Signup and view all the answers

What happens to the graph of the cosine function when the parameter $a$ is negative?

It reflects about the x-axis. Signup and view all the answers

What is the period of the tangent function $y = a \tan \theta + q$?

180° Signup and view all the answers

For the function $y = a \sin \theta + q$, what is the y-intercept when $\theta = 0$?

$a + q$ Signup and view all the answers

In the equation of a parabola $y = ax^2 + q$, what does the coefficient $a$ determine?

The direction of opening. Signup and view all the answers

Where are the asymptotes located for the tangent function $y = a \tan \theta + q$?

At $\theta = 90°$ and $270°$ Signup and view all the answers

What effect does the value of $q$ have on the trigonometric function $y = a \cos \theta + q$?

It causes a vertical shift. Signup and view all the answers

What is the range of the function $y = a \cos \theta + q$ when $a > 0$?

$[q - |a|, q + |a|]$ Signup and view all the answers

What is the significance of $b$ in the function $y = ab^x + q$ when $b > 1$?

It signifies exponential growth. Signup and view all the answers

What is the domain of the hyperbolic function of the form $y = \frac{a}{x} + q$?

${x : x \in \mathbb{R}, x \neq 0}$ Signup and view all the answers

If the parameter $q$ in the hyperbolic function $y = \frac{a}{x} + q$ is positive, how does it affect the graph?

The graph is shifted vertically upwards by $q$ units. Signup and view all the answers

What is the horizontal asymptote of the hyperbolic function $y = \frac{a}{x} + q$?

$y = q$ Signup and view all the answers

For the exponential function $y = ab^x + q$, what can be said about the range when $a < 0$?

The range is ${y : y < q}$ Signup and view all the answers

What effect does a negative value of $a$ have on the hyperbolic function's graph $y = \frac{a}{x} + q$?

The graph lies only in the second and fourth quadrants. Signup and view all the answers

In the exponential function $y = ab^x + q$, how is the y-intercept determined?

By setting $x = 0$ in the exponential formula. Signup and view all the answers

What is the effect of increasing the value of $q$ in the hyperbolic function $y = \frac{a}{x} + q$?

It causes the horizontal asymptote to move upwards. Signup and view all the answers

What is the vertical asymptote of the hyperbolic function of the form $y = \frac{a}{x} + q$?

$x = 0$ Signup and view all the answers

Which statement correctly describes the effect of $a$ when $a > 0$ in the exponential function $y = ab^x + q$?

The graph has a single horizontal asymptote at $y = q$. Signup and view all the answers

How is the x-intercept of the hyperbolic function $y = \frac{a}{x} + q$ calculated?

By setting $y = 0$ and solving for $x$. Signup and view all the answers

What can you determine about the value of 'a' in the equation of a parabola if the graph opens upwards?

'a' must be greater than zero Signup and view all the answers

How is the y-intercept found for a hyperbola described by the equation $y = \frac{a}{x} + q$?

Set 'x' equal to zero Signup and view all the answers

In the context of trigonometric functions, what does the vertical shift 'q' represent?

The amount by which the graph is lifted or lowered Signup and view all the answers

When performing calculations for the points of intersection of two graphs, which method is typically used?

Equating the expressions of both graphs Signup and view all the answers

What determines the shape of a hyperbola in the equation $y = \frac{a}{x} + q$?

The value of 'a' only Signup and view all the answers

For the function $y = a \sin \theta + q$, which statement is true when 'a' is negative?

The wave is reflected across the x-axis Signup and view all the answers

When determining the domain of the hyperbolic function $y = \frac{a}{x} + q$, which statement is accurate?

Domain cannot include zero Signup and view all the answers

Which method is NOT used when solving for 'a' and 'q' based on points provided in a trigonometric function?

Calculating the angles of the graph Signup and view all the answers

How does one typically determine vertical asymptotes in hyperbolas?

By setting the denominator equal to zero Signup and view all the answers

What characteristic do the coefficients of 'a' in parabolic equations represent?

The direction and width of the parabola Signup and view all the answers

What characteristic does the parameter 'a' provide to the graph of the function $y = ax^2 + q$?

Determines the direction and shape of the graph Signup and view all the answers

What happens to the graph of $y = ax^2 + q$ when the value of 'q' is increased?

The graph shifts vertically upwards Signup and view all the answers

What is the significance of the axis of symmetry in the function $y = ax^2 + q$?

It reflects the left half of the graph onto the right half Signup and view all the answers

If the coefficient 'a' of the parabola is negative, what does this indicate about the shape of the graph?

The graph opens downwards and has a maximum turning point Signup and view all the answers

When determining the y-intercept of the function $y = ax^2 + q$, what should be done with the variable 'x'?

Set $x = 0$ to find the corresponding value of $y$ Signup and view all the answers

In the general function form $y = mx + c$, which characteristic is crucial for sketching the graph using the dual intercept method?

Both the x-intercept and y-intercept are needed Signup and view all the answers

What scenario leads to a wider parabolic graph in the function $y = ax^2 + q$?

When $0 < a < 1$ Signup and view all the answers

How does the graph of $y = ax^2 + q$ behave when $q < 0$?

The entire graph shifts downwards Signup and view all the answers

What type of turning point does a parabola described by $y = ax^2 + q$ possess when $a > 0$?

A minimum turning point Signup and view all the answers

What is the range of the function $y = ax^2 + q$ when $a < 0$?

The range is $(- ext{infinity}; q]$ Signup and view all the answers

How does an increase in the value of 'm' affect the slope of the graph of a linear function?

It increases the slope. Signup and view all the answers

What characteristic of a straight line graph is determined by the y-intercept 'c' when 'c < 0'?

The graph shifts vertically downwards. Signup and view all the answers

When analyzing the equation $y = mx + c$, what effect does a negative value of 'm' imply for the orientation of the graph?

The graph slopes downwards from left to right. Signup and view all the answers

What is the domain of the function $f(x) = mx + c$?

All real numbers. Signup and view all the answers

In the context of linear functions, what does the term 'gradient' refer to?

The slope of the graph. Signup and view all the answers

If both m and c are zero in the equation $y = mx + c$, what can be said about the graph?

It is a horizontal line at the origin. Signup and view all the answers

What happens when 'c' is greater than zero in the equation of a linear function?

The graph shifts vertically upwards. Signup and view all the answers

In a linear function, how is the x-intercept calculated?

Set y equal to zero. Signup and view all the answers

What happens to the graph of the function when the coefficient 'a' is zero in the equation $y = ax^2 + q$?

The graph becomes a horizontal line. Signup and view all the answers

For the quadratic function $y = ax^2 + q$, what does a negative value of 'q' signify?

The minimum point will be below the x-axis. Signup and view all the answers

When the gradient 'm' in a linear function $y = mx + c$ is increased, what is the consequent change in the graph?

The line becomes steeper. Signup and view all the answers

How does the sign of 'a' affect the axis of symmetry of the parabolic function $y = ax^2 + q$?

It has no effect on the axis of symmetry. Signup and view all the answers

In the context of the quadratic function $y = ax^2 + q$, what is the behavior of the graph when $a$ is a small positive number (e.g., $0 < a < 1$)?

The graph becomes wider. Signup and view all the answers

What is indicated by the x-intercepts of the function $y = ax^2 + q$ when 'a' is negative?

There will be two x-intercepts. Signup and view all the answers

When calculating the y-intercept of a linear function $y = mx + c$, which of the following correctly defines the method?

Substituting $x = 0$ into the equation. Signup and view all the answers

In a graph of quadratic function $y = ax^2 + q$, what characteristic is associated with the minimum turning point when $a > 0$?

It is located at $(0, q)$. Signup and view all the answers

What is the correct method to find the x-intercepts of the quadratic function $y = ax^2 + q$?

Set $y = 0$ and solve the resulting equation. Signup and view all the answers

What happens to the graph of the hyperbolic function when the value of 'q' is negative?

The graph shifts vertically downwards by 'q' units Signup and view all the answers

In the context of hyperbolic functions, what does the horizontal asymptote indicate?

The y-values approach but never reach q Signup and view all the answers

For the exponential function $y = ab^x + q$, what does the sign of 'a' influence?

The direction of the curve (upwards or downwards) Signup and view all the answers

Which characteristic is true about the axes of symmetry for hyperbolic functions?

The lines are y = x + q and y = -x + q Signup and view all the answers

What is the effect of having 'a' greater than zero in the exponential function?

The graph will increase to infinity as x increases Signup and view all the answers

How does the vertical asymptote behave in the hyperbolic function $y = \frac{a}{x} + q$?

It is located at x = 0 Signup and view all the answers

When calculating the x-intercept of the hyperbolic function $y = \frac{a}{x} + q$, which statement is true?

Set y to 0 Signup and view all the answers

What is the interpretation of 'q' in the function $y = \frac{a}{x} + q$?

It denotes a vertical shift of the graph Signup and view all the answers

In exponential functions, what is the significance of the horizontal asymptote?

It indicates where the y-values stabilize Signup and view all the answers

What occurs when 'a' in the hyperbolic function $y = \frac{a}{x} + q$ is negative?

The graph lies in the second and fourth quadrants Signup and view all the answers

Which statement accurately describes how to identify the parameters of a hyperbola from its graph?

The sign of $a$ is deduced from recognizing the quadrants of the hyperbola. Signup and view all the answers

In determining the equation of a parabola, which method is not typically used?

Using the vertex coordinates to find $a$ and $q$. Signup and view all the answers

Which statement correctly characterizes the amplitude of trigonometric graphs?

It corresponds directly to the value of $a$ in the equation. Signup and view all the answers

What defines the vertical shift of a hyperbola as given by its equation?

The value of $q$. Signup and view all the answers

To find points of intersection between two graphs, which mathematical principle should be applied?

Set the equations equal and solve for both $x$ and $y$. Signup and view all the answers

In the context of the graph of $y = a an heta + q$, what does the parameter $q$ affect?

The vertical shift of the graph. Signup and view all the answers

Which characteristic feature is associated with the distance formula when calculating distances in graph interpretations?

It uses the differences of coordinates to measure distance. Signup and view all the answers

When solving for the parameters of trigonometric functions, what must be done with the systems of equations?

Simultaneous solutions should be derived to isolate $a$ and $q$. Signup and view all the answers

How do the asymptotes of a hyperbola inform about its graph behavior?

They indicate where the graph will never intersect the axis. Signup and view all the answers

Which of the following conditions is indicative of a parabola opening downwards?

The value of $a$ is less than zero. Signup and view all the answers

What effect does a value of $b$ between 0 and 1 have on the function $y = ab^x + q$?

It represents exponential decay. Signup and view all the answers

Which statement is true about the sine function $y = a ext{sin} heta + q$ when $|a| > 1$?

It has a vertical stretch effect. Signup and view all the answers

What conditions must be met for the function $y = a ext{tan} heta + q$ to experience an upward vertical shift?

When $q > 0$. Signup and view all the answers

In the context of the sine function, which points represent the maximum turning points?

(90°, 1) and (360°, 1) Signup and view all the answers

What describes the range of the function $y = a ext{cos} heta + q$ when $a < 0$?

[q - |a|, q + |a|] Signup and view all the answers

Which of the following statements about the tangent function $y = ext{tan} heta$ is correct?

The function has a period of 360°. Signup and view all the answers

Which characteristic is true for the horizontal asymptotes of an exponential function when $a < 0$?

They are located at $y = q$. Signup and view all the answers

What is the effect of a negative value for $a$ in the function $y = a ext{sin} heta + q$?

It reflects the graph about the x-axis. Signup and view all the answers

The vertical asymptotes of the tangent function occur at which angles?

90° and 270° Signup and view all the answers

For the function $y = a ext{tan} heta + q$, how does the value of $a$ affect the steepness of the branches?

The larger the value of $a$, the steeper the branches. Signup and view all the answers

What effect does an increase in the value of 'c' have on the graph of the function?

The graph will shift vertically upwards. Signup and view all the answers

Which statement accurately describes the behavior of the graph when 'm' is set to 0?

The graph becomes a horizontal line. Signup and view all the answers

In the equation of a linear function, what is the primary role of the parameter 'm'?

It describes the steepness or slope of the line. Signup and view all the answers

If 'c' is negative, what impact does this have on the graph of the function?

The graph shifts vertically downward. Signup and view all the answers

What does the equation obtain when determining the y-intercept of a straight-line function?

Set 'x' to zero and solve for 'y'. Signup and view all the answers

Which of the following accurately describes the domain of the function $f(x) = mx + c$?

The domain is all real numbers. Signup and view all the answers

What mathematical concept does the variable 'c' represent in the function $y = mx + c$?

The y-coordinate where the line intersects the y-axis. Signup and view all the answers

What indicates that a line has a negative slope when examining the function $y = mx + c$?

The line runs from the top left to the bottom right. Signup and view all the answers

What is the y-intercept of the function described by $y = a \sin \theta + q$?

$q$ Signup and view all the answers

For a function of the form $y = ab^x + q$ with $a < 0$ and $0 < b < 1$, what is the behavior of the graph?

The graph curves downwards and represents exponential decay. Signup and view all the answers

In the context of the sine function $y = a \sin \theta + q$, which condition indicates a vertical stretch?

$|a| > 1$ Signup and view all the answers

What describes the period of the tangent function $y = a \tan \theta + q$?

180° Signup and view all the answers

Which characteristic is true for the cosine function's maximum turning point in the form $y = a \cos \theta + q$?

Occurs at $(0°, 1)$ Signup and view all the answers

What is the range of the sine function $y = a \sin \theta + q$ when $a < 0$ and $q > 0$?

[q - |a|, q + |a|] Signup and view all the answers

What effect does a negative value of $a$ have on the graph of the cosine function $y = a \cos \theta + q$?

Causes a reflection about the x-axis. Signup and view all the answers

Where do the asymptotes of the tangent function $y = a \tan \theta + q$ occur?

$\theta = 90°, 270°$ Signup and view all the answers

What is the x-intercept of the function $y = a \sin \theta + q$?

$(0°, 0)$ and $(360°, 0)$ Signup and view all the answers

What can be said about the domain of the hyperbolic function of the form $y = \frac{a}{x} + q$?

It excludes zero. Signup and view all the answers

What is the behavior of the range of the function $y = ab^x + q$ when $a < 0$?

It is less than q. Signup and view all the answers

Which statement accurately describes the vertical asymptote of the hyperbolic function $y = \frac{a}{x} + q$?

It is at $x = 0$. Signup and view all the answers

What effect does a positive value of 'a' have on the hyperbolic function $y = \frac{a}{x} + q$?

It causes the graph to lie in the first and third quadrants. Signup and view all the answers

In the context of exponential functions, what does the value of 'q' affect?

The horizontal asymptote and shifts the graph vertically. Signup and view all the answers

How can the x-intercept of the hyperbolic function $y = \frac{a}{x} + q$ be calculated?

By setting y equal to zero. Signup and view all the answers

What is the effect of 'q' on the graph of an exponential function when $q < 0$?

It lowers the horizontal asymptote. Signup and view all the answers

What is the horizontal asymptote of the hyperbolic function $y = \frac{a}{x} + q$?

It is given by the line $y = q$. Signup and view all the answers

When sketching the graph of the function $y = \frac{a}{x} + q$, which characteristic is least likely to be useful?

The number of solutions of the equation. Signup and view all the answers

What is the key characteristic of the graph of the function when the parameter 'a' is greater than zero?

The graph opens upwards with a minimum turning point. Signup and view all the answers

Which of the following describes the effect of varying 'q' for a parabolic function?

It shifts the graph vertically without changing its shape. Signup and view all the answers

What happens to the graph of the function when 'a' is less than zero?

The graph results in a maximum turning point. Signup and view all the answers

How do the turning points of the graph change if 'a' gets closer to zero but remains positive?

They move vertically towards the horizontal axis. Signup and view all the answers

When calculating the x-intercept of a quadratic function, what must be true about the value of 'y'?

It must equal zero. Signup and view all the answers

What impact does the sign of 'm' have in the linear equation 'y = mx + c'?

It indicates the steepness and direction of the line. Signup and view all the answers

In the context of parabolic functions, what is the effect on the range when 'a' is negative?

The range extends only downwards. Signup and view all the answers

Which of the following statements accurately describes the axis of symmetry for a parabolic function?

It coincides with the y-axis for all parabolas. Signup and view all the answers

What is necessary to sketch a graph of the form 'y = ax^2 + q'?

The sign of 'a', as well as the intercepts and turning point. Signup and view all the answers

How can the sign of 'a' in a quadratic function affect the overall shape of the graph?

It also indicates if the parabola opens upwards or downwards. Signup and view all the answers

What characteristic of a hyperbola is determined by the value of parameter 'a' in the equation $y = \frac{a}{x} + q$?

The direction and shape of the hyperbola Signup and view all the answers

In the context of parabolas, how does the parameter 'q' affect the graph of the equation $y = ax^2 + q$?

It dictates the vertical shift of the parabola Signup and view all the answers

When interpreting a trigonometric graph, what is a crucial first step to determine the equation of the form $y = a \sin \theta + q$?

Identify the type of graph and its vertical shifts Signup and view all the answers

What does the y-intercept of a trigonometric function of the form $y = a \cos \theta + q$ indicate?

The vertical shift value of the cosine graph Signup and view all the answers

Which mathematical approach is most effective in solving for both 'a' and 'q' within a hyperbola's equation when given multiple points?

Substituting the values and solving simultaneously Signup and view all the answers

In the equation $y = \frac{a}{x} + q$, how can you determine the vertical shifts represented by 'q'?

Through the calculation of the y-intercepts Signup and view all the answers

What is necessary for calculating points of intersection between two graphs?

Equate their expressions and solve for corresponding values Signup and view all the answers

In determining the equation of a trigonometric function, which is a critical condition when 'a' is less than zero?

The graph reflects across the x-axis Signup and view all the answers

What is the primary role of asymptotes in the function $y = \frac{a}{x} + q$?

To indicate where the function approaches infinity Signup and view all the answers

What effect does the sign of $a$ have on the graph of the function $y = ax^2 + q$?

It affects the direction and width of the parabola. Signup and view all the answers

When determining the equation of a hyperbola, what do the quadrants where the curves lie indicate?

They help identify the sign of $a$. Signup and view all the answers

Which of the following steps is NOT necessary when solving for $a$ and $q$ from points in trigonometric functions?

Calculating the amplitude of the graph. Signup and view all the answers

In the context of hyperbolas, what role do asymptotes play?

They influence the behavior as $x$ approaches zero. Signup and view all the answers

How is the y-intercept found for the function $y = rac{a}{x} + q$?

By evaluating $q$ directly. Signup and view all the answers

Which statement correctly describes how to calculate intercepts for parabolic functions?

Calculate the y-intercept by setting $x = 0$. Signup and view all the answers

What method should be used to find the points of intersection between two graphs?

Equate the expressions of both graphs and solve for $x$ and $y$. Signup and view all the answers

What is indicated by the vertical shift $q$ in the functions $y = a an heta + q$?

It moves the graph up or down without affecting its shape. Signup and view all the answers

In the function $y = a ext{sin} heta + q$, how does the value of $a < 0$ affect the graph?

It reflects the graph across the x-axis. Signup and view all the answers

What characteristic is essential when examining the graph of $y = a ext{cos} heta + q$?

Noting any vertical shifts to ascertain $q$. Signup and view all the answers

Gr 10 Math Ch 5 SUM: Functions

Questions and Answers

What does the parameter 'm' represent in the equation of a straight line?

How does the value of 'c' affect the graph of the linear function?

If the value of 'm' is negative, which of the following is true about the graph?

What values can the range of the function f(x) = mx + c take?

If 'c' is greater than zero, how does it affect the position of the graph?

What is the equation used to calculate the x-intercept of a linear function?

Which statement accurately describes the domain of the function f(x) = mx + c?

In the context of straight-line functions, what happens when 'm' equals zero?

What characterizes the graph of the function when the value of b is greater than 1?

In the function of the form $y = a an \theta + q$, how does the value of a affect the graph?

Which point is identified as the minimum turning point in the sine function?

What is the range of the function $y = a ext{sin} \theta + q$ when $a > 0$?

Which of the following statements about the cosine function is true?

What is the primary effect of the parameter q in the function $y = a ext{cos} \theta + q$?

What is the period of the tangent function $y = a an \theta + q$?

In the function $y = ab^x + q$, what does the sign of a determine?

What is the domain of the hyperbolic function of the form $y = \frac{a}{x} + q$?

Where are the asymptotes for the function $y = an \theta$ located?

If $a < 0$ in a hyperbolic function, in which quadrants does the graph lie?

What happens to the graph of an exponential function when $q < 0$?

Which type of asymptote is found in the hyperbolic function $y = \frac{a}{x} + q$?

For the exponential function $y = ab^x + q$, if $a > 0$ and $b > 1$, what can be said about the behavior of the graph?

What do you need to determine first when sketching the graph of the form $y = mx + c$?

What characteristic feature is associated with the y-intercept of the hyperbolic function $y = \frac{a}{x} + q$?

In the equation $y = ax^2 + q$, what does the parameter $q$ represent?

How is the horizontal asymptote of an exponential function described?

How does the gradient $m$ affect the graph of $y = mx + c$?

What does the variable $q$ represent in the context of hyperbolic functions?

What happens to the parabola when $a < 0$ in the equation $y = ax^2 + q$?

In which case does the graph of a hyperbolic function intersect the x-axis?

If $a = 2$ in the function $y = ax^2 + q$, which statement is true regarding the shape of the parabola?

What feature distinguishes the axes of symmetry of hyperbolic functions?

What is the range of the function $y = ax^2 + q$ when $a > 0$?

To find the x-intercept of a parabola described by $y = ax^2 + q$, you need to:

What is the axiom of symmetry for parabolas represented by $f(x) = ax^2 + q$?

If $q < 0$ in the equation $y = ax^2 + q$, what does this indicate about the graph?

What does the coefficient $ a $ in the equation of a parabola determine?

How can you determine the value of $ q $ for a hyperbola given its equation?

To find the points of intersection between two graphs, what mathematical method should be applied?

In the equation of sine and cosine functions, how does the value of $ a $ affect the graph?

What is the primary method for calculating the y-intercept of a graph?

Which of the following statements about the equation of a hyperbola is true?

What role do asymptotes play in hyperbolas?

What does the distance formula primarily calculate between two points?

Which step is NOT involved when solving for $ a $ and $ q $ from given points in a trigonometric function?

What effect does the parameter 'b' have in the function of the form $y = ab^x + q$ when $b > 1$?

In a sine function described by $y = a ext{sin} heta + q$, what is the effect of $q$ when $q < 0$?

What happens to the period of the cosine function when represented in the form $y = rac{1}{2} ext{cos} heta + 1$?

What is indicated by the x-intercepts of the function $y = an heta$?

For the function $y = a ext{cos} heta + q$, what is the condition for vertical compression?

Which of the following describes the maximum turning point of the sine function $y = ext{sin} heta$?

What is the primary characteristic of the tangent function's graph?

What does the parameter 'a' influence in the function form $y = a ext{tan} heta + q$?

How does the sign of 'a' in the equation $y = ax^2 + q$ affect the parabola's orientation?

What describes the domain of the hyperbolic function of the form $y = \frac{a}{x} + q$?

Which of the following correctly describes the y-intercept of the hyperbolic function $y = \frac{a}{x} + q$?

What is the effect of the parameter 'm' when it is equal to zero in the function y = mx + c?

If $a > 0$ in the exponential function $y = ab^x + q$, what can be inferred about the graph's behavior?

What is the effect of changing the value of $q$ in the hyperbolic function $y = \frac{a}{x} + q$?

How does the y-intercept behave when 'c' is less than zero in the equation y = mx + c?

When the value of 'm' is positive, what can be said about the direction of the graph?

What characteristic feature distinguishes the range of the hyperbolic function $y = \frac{a}{x} + q$?

Considering the characteristics of the function f(x) = mx + c, what does the domain represent?

Which of the following statements is true regarding the asymptotes of the hyperbolic function?

If $a < 0$ in the hyperbolic function $y = \frac{a}{x} + q$, in which quadrants will the graph primarily lie?

What happens to the line represented by y = mx + c if the value of 'm' decreases from a positive to a negative value?

What is the x-intercept of the hyperbolic function $y = \frac{a}{x} + q$?

If c = 0 in the equation y = mx + c, what can be inferred about the graph?

What is true about the x-intercept of the function y = mx + c?

For exponential functions with the form $y = ab^x + q$, when $q < 0$, how is the graph's horizontal asymptote affected?

Which axis serves as the line of symmetry for the hyperbolic function $y = \frac{a}{x} + q$?

What effect does a larger value of 'm' have on the gradient of the linear function?

How can the x-intercept of the function in the form $y = ax^2 + q$ be calculated?

What happens to the graph when $a < 0$ in the equation $y = ax^2 + q$?

If the y-intercept $c$ in the equation $y = mx + c$ is greater than zero, where does the graph intersect the y-axis?

What characteristic describes the axis of symmetry in parabolic graphs of the form $y = ax^2 + q$?

What is the effect of the parameter $q$ in the quadratic function $y = ax^2 + q$?

What indicates whether the graph of $y = ax^2 + q$ has a minimum or maximum turning point?