Gr 10 Math Ch 5: Interpretation of Graphs

What effect does the parameter 'a' have on the graph of a parabola?

It has no effect on the graph.

It determines the shape of the x-intercepts.

It determines the vertical shift of the parabola.

It determines the direction and width of the parabola. (correct)

When calculating the y-intercept of a function, which value should be set to find it?

Set both $x$ and $y$ to zero.

Set $y = 0$ to find the y-intercept.

Set $x = 0$ to find the y-intercept. (correct)

Set the parameter 'a' to zero.

Which of the following statements about hyperbolas is true?

Hyperbolas always intersect the y-axis.

The shape of the hyperbola is unaffected by 'a'.

The parameter 'a' determines the direction and shape of the hyperbola. (correct)

The equation has no vertical shift component.

For trigonometric functions, what does the parameter 'q' do?

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

Which method is used to find the values of 'a' and 'q' when given points?

Substitute the points into the equations and solve simultaneously. Signup and view all the answers

What characterizes the asymptotes of hyperbolas?

Asymptotes are determined by setting the denominator of the function to zero. Signup and view all the answers

What is the first step in determining the equation of a parabola?

Examine the sketch to identify direction and vertical shifts Signup and view all the answers

How can you determine the constant q in the equation of a parabola?

Using the y-intercept point (0; y) Signup and view all the answers

What is necessary to solve for a in the equation of a hyperbola?

Another specific point on the hyperbola Signup and view all the answers

What information can be found by calculating the intercepts in a graph?

The coordinates where the graph intersects the axes Signup and view all the answers

To interpret trigonometric graphs, what aspect should be identified first?

The type of trigonometric graph and vertical shifts Signup and view all the answers

How are distances calculated when points are aligned vertically or horizontally?

By simple subtraction of the coordinates Signup and view all the answers

In the equation of a hyperbola, what determines the sign of a?

The quadrants where the curves are located Signup and view all the answers

Which formula explains how to find points of intersection for two graphs?

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

What effect does the parameter 'q' have on the graph of a hyperbola?

It determines the vertical shift of the hyperbola. Signup and view all the answers

Which of the following best describes the domain of a hyperbolic function?

All real numbers except where the denominator is zero. Signup and view all the answers

When evaluating the vertical shift of a trigonometric function like sine, which parameter is responsible?

The constant term 'q'. Signup and view all the answers

What is the characteristic shape of a parabola defined by the equation $y = ax^2 + q$ when 'a' is negative?

It opens downwards. Signup and view all the answers

How do you identify the y-intercept of a function given by $y = ax^2 + q$?

Substitute 0 for $x$ into the equation. Signup and view all the answers

In the context of functions, what role do asymptotes play for hyperbolas and tangent functions?

They act as guidelines that the function approaches but never touches. Signup and view all the answers

What is the method to find the y-intercept for a parabola?

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

Which of the following describes the first step in determining the equation of a hyperbola?

Identify the quadrants where the curves lie Signup and view all the answers

When determining the equation of a trigonometric function, what is the significance of the parameter 'q'?

It represents the vertical shift of the graph Signup and view all the answers

What method is used to solve for 'a' and 'q' in the hyperbola equation?

Solve simultaneously using substitution Signup and view all the answers

Which of the following is true about calculating intercepts for graphs?

x-intercepts are found by setting y to 0 Signup and view all the answers

What is the role of the sketch in determining the equation of a parabola?

It helps identify the opening direction and vertical shift Signup and view all the answers

In calculating points of intersection between two graphs, what must be done?

Equate the expressions and solve for both x and y Signup and view all the answers

When examining a trigonometric graph, what is crucial to observe first?

The shift and type of graph (sine or cosine) Signup and view all the answers

What effect does changing the value of 'a' in the equation of a hyperbola, $y = \frac{a}{x} + q$, have on its graph?

It alters the direction and shape of the hyperbola. Signup and view all the answers

How can the range of a trigonometric function described by $y = a \sin \theta + q$ be defined when 'a' is negative?

All values above q up to q - |a|. Signup and view all the answers

In the context of graphing parabolas, how does the value of 'q' impact the graph represented by $y = ax^2 + q$?

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

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

It includes all real numbers except for x = 0. Signup and view all the answers

What is the significance of asymptotes in the graph of hyperbolic functions?

They define boundaries that the graph approaches but never crosses. Signup and view all the answers

When solving simultaneous equations to find values of 'a' and 'q', which method is primarily used?

Substituting values from one equation into the other. Signup and view all the answers

Which of the following correctly describes the steps to determine the equation of a parabola?

Examine the sketch, determine q using the y-intercept, then use another point to find a. Signup and view all the answers

What is the best method to find the values of a and q in the hyperbola equation?

Substitute known points into the hyperbola equation and solve the resulting equations simultaneously. Signup and view all the answers

When calculating points of intersection between two graphs, what is the initial step?

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

Which of the following best explains how to calculate the y-intercept of a function?

Set x to 0 and solve for y. Signup and view all the answers

What strategy is used to determine the sign of 'a' in the equation of a hyperbola?

Identify the quadrants where the curves reside. Signup and view all the answers

Which of the following describes the relationship between the parameters 'a' and 'q' in trigonometric functions?

'a' indicates the amplitude, whereas 'q' denotes vertical shifts. Signup and view all the answers

What is the significance of the y-intercept in determining the equation of a parabola?

It provides the value of q directly. Signup and view all the answers

To accurately portray a trigonometric function's graph, what is the most critical initial observation?

The vertical shifts indicated by q. Signup and view all the answers

What effect does the parameter 'a' have on the graph of the sine function given by the equation $y = a \sin \theta + q$?

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

In the equation of a hyperbola $y = \frac{a}{x} + q$, how does changing the value of 'q' influence the graph?

It affects the vertical shift of the graph. Signup and view all the answers

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

The domain includes all real numbers except for zero. Signup and view all the answers

What is the primary role of asymptotes in the graph of a hyperbolic function?

They help identify the limits of the function as it approaches infinity. Signup and view all the answers

In the context of trigonometric functions, how does the parameter 'a' in the equation $y = a \cos \theta + q$ primarily affect the graph?

It alters the amplitude of the cosine wave. Signup and view all the answers