Gr 11 Math Ch 5 SUM: Functions

What is the effect of the parameter $p$ on the graph of $y = a(x + p)^2 + q$?

Horizontal shift

What is the turning point of the graph of $y = ax^2 + q$ when $a > 0$ and $q > 0$?

Minimum turning point above the x-axis

What happens to the graph of $y = ax^2 + q$ when $a$ becomes larger?

The graph becomes narrower

What is the effect of the parameter $q$ on the graph of $y = a(x + p)^2 + q$?

Vertical shift Signup and view all the answers

What is the shape of the graph of $y = a(x + p)^2 + q$ when $a < 0$?

A 'frown' with a maximum turning point Signup and view all the answers

What is the axis of symmetry of the graph of $y = a(x + p)^2 + q$?

The line $x = -p$ Signup and view all the answers

What is the y-intercept of the graph of $y = ax^2 + q$?

$q$ Signup and view all the answers

What happens to the graph of $y = a(x + p)^2 + q$ when $a = 0$?

The graph becomes a horizontal line $y = q$ Signup and view all the answers

What is the effect of a change in p on the graph of y = a/(x + p) + q?

The graph is shifted horizontally by p units. Signup and view all the answers

What is the vertical asymptote of the hyperbola y = a/(x + p) + q?

x = -p Signup and view all the answers

What is the range of the function y = ab^x + q, if a > 0?

{y: y > q, y ∈ ℝ} Signup and view all the answers

What is the effect of a on the shape of the graph of y = ab^x + q?

If a < 0, the graph is reflected about the horizontal asymptote. Signup and view all the answers

What is the effect of q on the graph of y = a/(x + p) + q?

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

What is the horizontal asymptote of the graph of y = ab^(x+p) + q?

y = q Signup and view all the answers

What is the range of the function y = a/(x + p) + q?

{y: y ≠ q, y ∈ ℝ} Signup and view all the answers

What is the domain of a quadratic function?

All real numbers Signup and view all the answers

What is the effect of p on the graph of y = ab^(x+p) + q?

The graph is shifted horizontally by p units. Signup and view all the answers

What is the range of the quadratic function f(x) = ax^2 + bx + c, where a > 0?

All real numbers greater than or equal to the y-coordinate of the vertex Signup and view all the answers

What is the x-intercept of the graph of y = a/(x + p) + q?

Set y = 0 Signup and view all the answers

What is the x-intercept of the quadratic function f(x) = ax^2 + bx + c?

The solution to f(x) = 0 Signup and view all the answers

What is the equation of the axis of symmetry of the quadratic function f(x) = a(x + p)^2 + q?

x = -p Signup and view all the answers

What is the effect of a on the graph of y = ab^(x+p) + q, if a < 0?

The graph lies below the horizontal asymptote. Signup and view all the answers

What is the effect of replacing x with x - m in the equation of a parabola?

A horizontal shift to the left by m units Signup and view all the answers

What is the average gradient of a curve between two points?

The gradient of the line passing through the two points Signup and view all the answers

What is the formula for the average gradient of a curve?

(f(a + h) - f(a)) / h Signup and view all the answers

What is the effect of q on the graph of the hyperbolic function y = a/x + q?

A vertical shift by q units Signup and view all the answers

What is the horizontal asymptote of the hyperbolic function y = a/x + q?

The line y = q Signup and view all the answers

What is the effect of a on the shape and quadrants of the graph of the hyperbolic function y = a/x + q?

For a > 0, the graph lies in the first and third quadrants Signup and view all the answers

What is the period of the sine function y = sinθ?

360° Signup and view all the answers

What is the amplitude of the sine function y = sinθ?

1 Signup and view all the answers

What is the effect of q on the graph of y = a sinθ + q?

Vertical shift Signup and view all the answers

What is the effect of k on the period of the sine function y = sin kθ?

The period decreases Signup and view all the answers

What is the period of the function y = tanθ?

180° Signup and view all the answers

What is the domain of the function y = tanθ?

{θ: 0° ≤ θ ≤ 360°, θ ≠ 90°, 270°} Signup and view all the answers

What is the x-intercept of the sine function y = sinθ?

(270°, 0) Signup and view all the answers

What is the effect of a on the shape of the graph of y = a tanθ?

a vertically stretches the graph Signup and view all the answers

What is the effect of a on the amplitude of the sine function y = a sinθ?

The amplitude increases Signup and view all the answers

What is the effect of k on the period of the function y = tan kθ?

the period is 180°/k Signup and view all the answers

What is the period of the cosine function y = cosθ?

360° Signup and view all the answers

What is the effect of p on the graph of y = cos(θ + p)?

Horizontal shift to the left Signup and view all the answers

What is the range of the function y = tan kθ?

{f(θ): f(θ) ∈ ℝ} Signup and view all the answers

What is the effect of p on the graph of y = tan(θ + p)?

p horizontally shifts the graph Signup and view all the answers

What is the maximum turning point of the cosine function y = cosθ?

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

What is the y-intercept of the cosine function y = cosθ?

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

What is the x-intercept of the graph of y = tan kθ?

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

What is the y-intercept of the graph of y = tan kθ?

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

What is the effect of a horizontal shift on the graph of y = a(x + p)^2 + q?

A vertical shift occurs Signup and view all the answers

What is the shape of the graph of y = a(x + p)^2 + q when a = 1 and q < 0?

A smile Signup and view all the answers

What happens to the graph of y = ax^2 + q when a becomes smaller?

The graph becomes wider Signup and view all the answers

What is the turning point of the graph of y = ax^2 + q when a < 0 and q > 0?

Above the x-axis Signup and view all the answers

What is the effect of p on the axis of symmetry of the graph of y = a(x + p)^2 + q?

The axis of symmetry is shifted to the right Signup and view all the answers

What happens to the graph of y = ax^2 + q when q becomes larger?

The graph is shifted vertically upwards Signup and view all the answers

What is the shape of the graph of y = a(x + p)^2 + q when a < 0 and q > 0?

A frown Signup and view all the answers

What happens to the graph of y = ax^2 + q when a becomes larger?

The graph becomes narrower Signup and view all the answers

What is the domain of a quadratic function?

(-∞, ∞) Signup and view all the answers

What is the range of the function y = a(x + p)^2 + q, if a > 0?

[q, ∞) Signup and view all the answers

What is the turning point of the graph of y = a(x + p)^2 + q?

(p, q) Signup and view all the answers

What is the effect of a horizontal shift of m units to the right on the graph of y = ax^2 + bx + c?

Replace x with x - m Signup and view all the answers

What is the average gradient of a curve between two points A(x_A, y_A) and C(x_C, y_C)?

y_C - y_A / x_C - x_A Signup and view all the answers

What is the vertical asymptote of the hyperbolic function y = a/(x + p) + q?

x = -p Signup and view all the answers

What is the effect of a on the shape of the graph of y = a/(x + p) + q?

It affects the shape and quadrants of the graph Signup and view all the answers

What is the equation of the axis of symmetry of the graph of y = a(x + p)^2 + q?

x = p Signup and view all the answers

How do you find the x-intercept of a quadratic function?

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

What is the effect of a horizontal shift of n units upwards on the graph of y = a(x + p)^2 + q?

Replace y with y + n Signup and view all the answers

What is the period of the sine function y = sin kθ?

360°/k Signup and view all the answers

What is the effect of a on the amplitude of the sine function y = a sin θ?

a increases the amplitude Signup and view all the answers

What is the y-intercept of the sine function y = sin θ?

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

What is the effect of q on the graph of y = a sin θ + q?

q shifts the graph vertically Signup and view all the answers

What is the range of the sine function y = sin θ?

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

What is the period of the cosine function y = cos kθ?

360°/k Signup and view all the answers

What is the effect of a on the shape of the graph of y = a cos θ?

a increases the amplitude Signup and view all the answers

What is the x-intercept of the cosine function y = cos θ?

(90°, 0) Signup and view all the answers

What is the effect of p on the graph of y = cos(θ + p)?

p shifts the graph horizontally Signup and view all the answers

What is the maximum turning point of the cosine function y = cos θ?

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

What is the period of the function y = tanθ?

180° Signup and view all the answers

What is the effect of a on the shape of the graph of y = a tanθ?

For a > 1, the branches of the graph are steeper. Signup and view all the answers

What is the effect of k on the period of the function y = tan kθ?

The period decreases as k increases. Signup and view all the answers

What is the domain of the function y = tan kθ?

The set of real numbers such that -90°/k < θ < 90°/k. Signup and view all the answers

What is the effect of q on the graph of y = a tanθ + q?

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

What is the range of the function y = tan kθ?

All real numbers. Signup and view all the answers

What is the effect of p on the graph of y = tan(θ + p)?

The graph is shifted horizontally by p units. Signup and view all the answers

What is the y-intercept of the graph of y = tan kθ?

(0, 0) Signup and view all the answers

What is the effect of a change in a on the shape of the graph of y = a/(x + p) + q?

The graph is reflected about the y-axis. Signup and view all the answers

What is the domain of the function y = a/(x + p) + q?

The domain is all real numbers except x = -p. Signup and view all the answers

What is the vertical asymptote of the graph of y = ab^x + q?

There is no vertical asymptote. Signup and view all the answers

What is the effect of a change in p on the graph of y = ab^(x+p) + q?

The graph is shifted horizontally to the right. Signup and view all the answers

What is the range of the function y = ab^x + q, if a > 0?

The range is all real numbers greater than q. Signup and view all the answers

What is the axis of symmetry of the hyperbola y = a/(x + p) + q?

The axis of symmetry is the line x = -p. Signup and view all the answers

What is the effect of a change in q on the graph of y = a/(x + p) + q?

The graph is shifted vertically upwards. Signup and view all the answers

What is the horizontal asymptote of the graph of y = ab^(x+p) + q?

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

What is the effect of a change in a on the range of the function y = a/(x + p) + q?

The range remains the same. Signup and view all the answers

What is the x-intercept of the graph of y = ab^x + q?

The x-intercept is the point where y = 0. Signup and view all the answers

What is the effect of a negative value of a on the graph of y = ax^2 + q?

The graph is a 'frown' and has a maximum turning point. Signup and view all the answers

What is the effect of a positive value of q on the graph of y = ax^2 + q?

The graph is shifted vertically upwards. Signup and view all the answers

What happens to the graph of y = ax^2 + q when a becomes larger?

The graph becomes narrower. Signup and view all the answers

What is the effect of a positive value of p on the graph of y = a(x + p)^2 + q?

The graph is shifted to the left by p units. Signup and view all the answers

What is the axis of symmetry of the graph of y = a(x + p)^2 + q?

The line x = -p. Signup and view all the answers

What is the effect of a on the graph of y = ax^2 + q when a is close to 0?

The graph becomes wider. Signup and view all the answers

What is the turning point of the graph of y = a(x + p)^2 + q?

(-p, q). Signup and view all the answers

What is the effect of a on the graph of y = a(x + p)^2 + q when a is negative?

The graph is a 'frown' and has a maximum turning point. Signup and view all the answers

What is the effect of a change in the parameter a on the shape of the graph of y = a/x + q?

The graph is stretched or compressed. Signup and view all the answers

What is the domain of the function y = ab^x + q?

All real numbers. Signup and view all the answers

What is the horizontal asymptote of the graph of y = ab^(x+p) + q?

The line y = q. Signup and view all the answers

What is the effect of a change in the parameter p on the graph of y = ab^(x+p) + q?

The graph is shifted horizontally. Signup and view all the answers

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

All real numbers greater than q. Signup and view all the answers

What is the vertical asymptote of the hyperbola y = a/(x + p) + q?

The line x = -p. Signup and view all the answers

What is the effect of a change in the parameter q on the graph of y = a/(x + p) + q?

The graph is shifted vertically. Signup and view all the answers

What is the period of the function y = sin(kθ)?

360° / k Signup and view all the answers

What is the axis of symmetry of the hyperbola y = a/(x + p) + q?

The point (-p, q). Signup and view all the answers

What is the effect of a change in the parameter a on the graph of y = ab^(x+p) + q?

The graph is stretched or compressed. Signup and view all the answers

What is the effect of a on the amplitude of the function y = a sin(θ)?

The amplitude is multiplied by a Signup and view all the answers

What is the range of the function y = sin(kθ)?

[-1, 1] Signup and view all the answers

What is the y-intercept of the graph of y = ab^x + q?

The point (0, q). Signup and view all the answers

What is the effect of p on the graph of y = sin(θ + p)?

The graph shifts to the left by p units Signup and view all the answers

What is the effect of a on the shape of the graph of y = a cos(θ)?

The amplitude is multiplied by a and the graph is unaffected Signup and view all the answers

What is the y-intercept of the graph of y = cos(θ)?

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

What is the period of the function y = cos(kθ)?

360° / k Signup and view all the answers

What is the effect of p on the graph of y = cos(θ + p)?

The graph shifts to the left by p units Signup and view all the answers

What is the domain of the function y = sin(kθ)?

{θ : θ ∈ ℝ} Signup and view all the answers

What is the x-intercept of the graph of y = sin(θ)?

(180°, 0) Signup and view all the answers

For a quadratic function f(x) = ax^2 + bx + c, how do you find the x-intercept(s)?

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

What is the vertical asymptote of the hyperbolic function y = a/(x + p) + q?

x = 0 Signup and view all the answers

What is the effect of shifting a parabola m units to the right?

Replace x with x - m in the equation. Signup and view all the answers

What is the formula for calculating the average gradient of a curve?

gradient = (y2 - y1) / (x2 - x1) Signup and view all the answers

What is the effect of a on the shape of the graph of the hyperbolic function y = a/x + q?

For a > 0, the graph lies in the first and third quadrants. Signup and view all the answers

How do you find the y-intercept of a quadratic function f(x) = ax^2 + bx + c?

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

What is the effect of a horizontal shift on the graph of y = a(x + p)^2 + q?

The graph is shifted horizontally by p units. Signup and view all the answers

What is the axis of symmetry of the graph of y = a(x + p)^2 + q?

The vertical line x = -p. Signup and view all the answers

What is the average gradient of a curve between two points A(a, f(a)) and Q(a + h, f(a + h))?

Gradient = (f(a + h) - f(a)) / h Signup and view all the answers

What is the effect of q on the graph of the hyperbolic function y = a/x + q?

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

What is the period of the tangent function y = tanθ?

180° Signup and view all the answers

What is the effect of the parameter q on the graph of y = a tanθ + q?

Vertical shift Signup and view all the answers

What is the domain of the function y = tan kθ?

θ ≠ 90°/k, 270°/k Signup and view all the answers

What is the effect of the parameter k on the period of the function y = tan kθ?

The period decreases Signup and view all the answers

What is the effect of a on the shape of the graph of y = a tanθ?

The branches of the graph are steeper Signup and view all the answers

What is the effect of the parameter p on the graph of y = tan(θ + p)?

Horizontal shift Signup and view all the answers

What is the y-intercept of the graph of y = tan kθ?

(0, 0) Signup and view all the answers

What is the range of the function y = tan kθ?

All real values of y Signup and view all the answers

What is the effect of a on the amplitude of the sine function y = a sinθ?

The amplitude increases Signup and view all the answers

What is the effect of k on the period of the cosine function y = cos kθ?

The period decreases Signup and view all the answers

What is the y-intercept of the graph of y = sinθ?

(0, 0) Signup and view all the answers

What is the effect of p on the graph of y = sin(θ + p)?

The graph shifts horizontally to the left Signup and view all the answers

What is the range of the cosine function y = cosθ?

[-1, 1] Signup and view all the answers

What is the effect of a on the shape of the graph of y = a cosθ?

The amplitude increases Signup and view all the answers

What is the x-intercept of the graph of y = cosθ?

(90, 0) Signup and view all the answers

What is the period of the function y = sin kθ?

360°/k Signup and view all the answers

What is the effect of q on the graph of y = a sinθ + q?

The graph shifts vertically upwards Signup and view all the answers

What is the maximum turning point of the sine function y = sinθ?

(90, 1) Signup and view all the answers

What is the effect of a on the shape of the graph of y = a tanθ?

The branches of the graph are steeper. Signup and view all the answers

What is the period of the graph of y = tan kθ?

180°/k Signup and view all the answers

What is the effect of p on the graph of y = tan(θ + p)?

A horizontal shift occur. Signup and view all the answers

What is the range of the graph of y = tan kθ?

(-∞, ∞) Signup and view all the answers

What is the domain of the graph of y = tan kθ?

{θ : -90°/k < θ < 90°/k, θ ∈ ℝ} Signup and view all the answers

What is the effect of k on the period of the graph of y = tan kθ?

The period decreases. Signup and view all the answers

What is the x-intercept of the graph of y = tan kθ?

0° Signup and view all the answers

What is the y-intercept of the graph of y = tan kθ?

0 Signup and view all the answers

What is the effect of the parameter $a$ on the graph of $y = a/x + q$?

A change in shape and quadrants Signup and view all the answers

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

{ $y : y < q, y \in \mathbb{R} $} Signup and view all the answers

What is the effect of replacing x with x - m in the equation of a parabola?

Horizontal shift to the left by m units. Signup and view all the answers

What is the axis of symmetry of the graph of $y = ab^{(x+p)} + q$?

The line $x = -p$ Signup and view all the answers

What is the axis of symmetry of the graph of y = a(x + p)^2 + q?

The vertical line x = -p. Signup and view all the answers

What happens to the graph of $y = a/x + q$ when $a$ tends to 0?

The graph moves closer to the axes Signup and view all the answers

What is the effect of a on the shape of the graph of y = a/(x + p) + q?

A larger value of a increases the steepness of the graph. Signup and view all the answers

What is the effect of a change in $p$ on the graph of $y = ab^{(x+p)} + q$?

A horizontal shift Signup and view all the answers

What is the average gradient of a curve between two points A and C?

The gradient of the line passing through points A and C. Signup and view all the answers

What is the horizontal asymptote of the graph of $y = a/(x + p) + q$?

The line $y = q$ Signup and view all the answers

What is the domain of the function $y = a/(x + p) + q$?

{ $x : x eq -p, x \in \mathbb{R} $} Signup and view all the answers

What is the effect of q on the graph of y = a/(x + p) + q?

A larger value of q shifts the graph vertically upwards. Signup and view all the answers

What is the formula for the average gradient of a curve?

Gradient = (y2 - y1) / (x2 - x1) Signup and view all the answers

What is the effect of a change in $q$ on the graph of $y = ab^x + q$?

A vertical shift Signup and view all the answers

What is the horizontal asymptote of the graph of y = a/(x + p) + q?

The line y = q. Signup and view all the answers

What is the axis of symmetry of the hyperbola $y = a/x + q$?

The line $y = q$ Signup and view all the answers

What is the effect of a change in $a$ on the graph of $y = a/(x + p) + q$?

A change in shape and quadrants Signup and view all the answers

What is the effect of a on the shape and quadrants of the graph of y = a/(x + p) + q?

A positive value of a results in a graph in the first and third quadrants. Signup and view all the answers

What is the vertical asymptote of the graph of y = a/(x + p) + q?

The line x = -p. Signup and view all the answers

What is the effect of a horizontal shift on the graph of y = a(x + p)^2 + q?

The graph is shifted horizontally to the left by p units. Signup and view all the answers

What is the effect of a negative value of $a$ on the graph of $y = a(x + p)^2 + q$?

It changes the graph from a 'smile' to a 'frown' Signup and view all the answers

What is the horizontal shift of the graph of $y = a(x + 2)^2 + q$?

2 units to the left Signup and view all the answers

What is the vertical shift of the graph of $y = ax^2 + 3$?

3 units upwards Signup and view all the answers

What is the effect of a positive value of $q$ on the graph of $y = ax^2 + q$?

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

What is the equation of the axis of symmetry of the graph of $y = a(x + p)^2 + q$?

x = -p Signup and view all the answers

What happens to the graph of $y = ax^2 + q$ when $a$ becomes smaller?

The graph becomes wider Signup and view all the answers

What is the turning point of the graph of $y = ax^2 + q$ when $a > 0$ and $q < 0$?

A minimum point below the x-axis Signup and view all the answers

What is the effect of a horizontal shift on the graph of $y = a(x + p)^2 + q$?

It shifts the graph horizontally Signup and view all the answers

What is the effect of a change in p on the graph of y = a/(x + p) + q?

A horizontal shift only. Signup and view all the answers

What is the equation of the vertical asymptote of the graph of y = a/(x + p) + q?

x = -p Signup and view all the answers

What is the effect of a change in q on the graph of y = a/(x + p) + q?

A vertical shift only. Signup and view all the answers

What is the range of the function y = ab^x + q?

All real numbers except q Signup and view all the answers

What is the effect of a change in a on the graph of y = ab^x + q?

A reflection about the horizontal asymptote. Signup and view all the answers

What is the equation of the horizontal asymptote of the graph of y = ab^(x+p) + q?

y = q Signup and view all the answers

What is the domain of the function y = a/(x + p) + q?

All real numbers except -p Signup and view all the answers

What is the effect of a change in p on the graph of y = ab^(x+p) + q?

A horizontal shift only. Signup and view all the answers

What is the axis of symmetry of the hyperbola y = a/(x + p) + q?

The line x = -p Signup and view all the answers

What is the range of the function y = a/(x + p) + q?

All real numbers except q Signup and view all the answers

What is the effect of a on the shape of the graph of y = a tan θ?

The graph becomes steeper and curves less Signup and view all the answers

What is the period of the graph of y = tan kθ when k = 2?

90° Signup and view all the answers

What is the asymptote of the graph of y = tan θ?

The lines θ = 90° and θ = 270° Signup and view all the answers

What is the effect of p on the graph of y = tan(θ + p)?

The graph shifts horizontally to the right by p units Signup and view all the answers

What is the domain of the graph of y = tan kθ?

{θ : 0° ≤ θ ≤ 360°, θ ≠ 90°, 270°} Signup and view all the answers

What is the range of the graph of y = tan kθ?

{f(θ) : f(θ) ∈ ℝ} Signup and view all the answers

What is the y-intercept of the graph of y = tan kθ?

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

What is the effect of k on the period of the graph of y = tan kθ?

The period decreases as k increases Signup and view all the answers

What is the expression for the average gradient of a curve between two points A(x_A, y_A) and C(x_C, y_C)?

Gradient = (y_A - y_C) / (x_A - x_C) Signup and view all the answers

What is the effect of the parameter $k$ on the period of the function $y = \sin k heta$?

The period is divided by $|k|$ Signup and view all the answers

What is the effect of a on the shape of the graph of the hyperbolic function y = a/x + q?

For a > 0, the graph lies in the first and third quadrants. Signup and view all the answers

What is the range of the function $y = a \sin heta + q$?

$[q-1, q+1]$ Signup and view all the answers

What is the axis of symmetry of the graph of the quadratic function y = a(x + p)^2 + q?

The axis of symmetry is the line x = -p. Signup and view all the answers

What is the effect of a horizontal shift on the graph of y = a(x + p)^2 + q?

The graph is shifted horizontally to the right by p units. Signup and view all the answers

What is the effect of the parameter $a$ on the amplitude of the function $y = a \sin heta$?

The amplitude is multiplied by $a$ Signup and view all the answers

What is the turning point of the quadratic function y = a(x + p)^2 + q?

The turning point is (p, q). Signup and view all the answers

What is the $y$-intercept of the graph of $y = \cos heta$?

$(0^\circ, 1)$ Signup and view all the answers

What is the effect of q on the graph of the quadratic function y = a(x + p)^2 + q?

For q > 0, the graph is shifted vertically upwards by q units. Signup and view all the answers

What is the effect of the parameter $p$ on the graph of $y = \cos( heta + p)$?

The graph is shifted horizontally by $p$ units Signup and view all the answers

What is the period of the function $y = \cos k heta$?

$\frac{360^\circ}{|k|}$ Signup and view all the answers

What is the domain of the quadratic function y = a(x + p)^2 + q?

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

What is the domain of the function $y = \cos k heta$?

${ heta : heta \in \mathbb{R} }$ Signup and view all the answers

What is the effect of a on the shape of the graph of the quadratic function y = a(x + p)^2 + q?

For a > 0, the graph opens upwards. Signup and view all the answers

What is the $x$-intercept of the graph of $y = \sin heta$?

$(180^\circ, 0)$ Signup and view all the answers

What is the range of the quadratic function y = a(x + p)^2 + q?

The range is all real numbers greater than or equal to q. Signup and view all the answers

What is the equation of the axis of symmetry of the quadratic function y = a(x - p)^2 + q?

The axis of symmetry is the line x = p. Signup and view all the answers

What is the effect of the parameter $a$ on the shape of the graph of $y = a \cos heta$?

The amplitude of the graph is multiplied by $a$ Signup and view all the answers

What is the minimum turning point of the graph of $y = \cos heta$?

$(180^\circ, -1)$ Signup and view all the answers

What is the effect of the parameter $a$ on the graph of $y = ax^2 + q$ when $a$ and $q$ are both negative?

The graph is a "frown" and has a maximum turning point. Signup and view all the answers

What happens to the graph of $y = a(x + p)^2 + q$ when $p$ is positive and $a$ is negative?

The graph is shifted to the left by $p$ units. Signup and view all the answers

What is the axis of symmetry of the graph of $y = a(x + p)^2 + q$ when $a$ and $q$ are both positive?

The line $x = -p$. Signup and view all the answers

What happens to the graph of $y = ax^2 + q$ when $a$ becomes smaller and $q$ is negative?

The graph becomes wider and the turning point is below the x-axis. Signup and view all the answers

What is the effect of the parameter $p$ on the graph of $y = a(x + p)^2 + q$ when $p$ is negative and $a$ is positive?

The graph is shifted to the right by $p$ units. Signup and view all the answers

What is the turning point of the graph of $y = ax^2 + q$ when $a$ and $q$ are both positive?

The point $(0, q)$. Signup and view all the answers

What happens to the graph of $y = a(x + p)^2 + q$ when $a$ becomes larger and $p$ is negative?

The graph becomes narrower and the turning point is to the left of the y-axis. Signup and view all the answers

What is the effect of the parameter $q$ on the graph of $y = ax^2 + q$ when $a$ and $q$ are both negative?

The graph is shifted vertically downwards. Signup and view all the answers

What is the effect of k on the period of the function y = tan kθ?

The period of the function is 180°/|k| Signup and view all the answers

What is the domain of the function y = tan kθ?

The domain of the function is the set of all real numbers except θ = 90° and θ = 270° Signup and view all the answers

What is the effect of a on the shape of the graph of y = a tanθ?

For a > 1, the branches of the graph are steeper Signup and view all the answers

What is the effect of q on the graph of y = a tanθ + q?

For q > 0, the graph is shifted vertically upwards by q units Signup and view all the answers

What is the equation of the asymptote of the graph of y = tanθ?

θ = 90° Signup and view all the answers

What is the x-intercept of the graph of y = tanθ?

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

What is the effect of p on the graph of y = tan(θ + p)?

For p > 0, the graph is shifted horizontally to the left by p units Signup and view all the answers

What is the period of the function y = tanθ?

The period of the function is 180° Signup and view all the answers

What is the range of the function y = tanθ?

The range of the function is the set of all real numbers Signup and view all the answers

What is the effect of a on the y-intercept of the graph of y = a tanθ?

For a > 0, the y-intercept is (0, 0) Signup and view all the answers

Gr 11 Math Ch 5 SUM: Functions

Questions and Answers

What is the effect of the parameter $p$ on the graph of $y = a(x + p)^2 + q$?

What is the turning point of the graph of $y = ax^2 + q$ when $a > 0$ and $q > 0$?

What happens to the graph of $y = ax^2 + q$ when $a$ becomes larger?

What is the effect of the parameter $q$ on the graph of $y = a(x + p)^2 + q$?

What is the shape of the graph of $y = a(x + p)^2 + q$ when $a < 0$?

What is the axis of symmetry of the graph of $y = a(x + p)^2 + q$?

What is the y-intercept of the graph of $y = ax^2 + q$?

What happens to the graph of $y = a(x + p)^2 + q$ when $a = 0$?

What is the effect of a change in p on the graph of y = a/(x + p) + q?

What is the vertical asymptote of the hyperbola y = a/(x + p) + q?

What is the range of the function y = ab^x + q, if a > 0?

What is the effect of a on the shape of the graph of y = ab^x + q?

What is the effect of q on the graph of y = a/(x + p) + q?

What is the horizontal asymptote of the graph of y = ab^(x+p) + q?

What is the range of the function y = a/(x + p) + q?

What is the domain of a quadratic function?

What is the effect of p on the graph of y = ab^(x+p) + q?

What is the range of the quadratic function f(x) = ax^2 + bx + c, where a > 0?

What is the x-intercept of the graph of y = a/(x + p) + q?

What is the x-intercept of the quadratic function f(x) = ax^2 + bx + c?

What is the equation of the axis of symmetry of the quadratic function f(x) = a(x + p)^2 + q?

What is the effect of a on the graph of y = ab^(x+p) + q, if a < 0?

What is the effect of replacing x with x - m in the equation of a parabola?

What is the average gradient of a curve between two points?

What is the formula for the average gradient of a curve?

What is the effect of q on the graph of the hyperbolic function y = a/x + q?

What is the horizontal asymptote of the hyperbolic function y = a/x + q?

What is the effect of a on the shape and quadrants of the graph of the hyperbolic function y = a/x + q?

What is the period of the sine function y = sinθ?

What is the amplitude of the sine function y = sinθ?

What is the effect of q on the graph of y = a sinθ + q?

What is the effect of k on the period of the sine function y = sin kθ?

What is the period of the function y = tanθ?

What is the domain of the function y = tanθ?

What is the x-intercept of the sine function y = sinθ?

What is the effect of a on the shape of the graph of y = a tanθ?

What is the effect of a on the amplitude of the sine function y = a sinθ?

What is the effect of k on the period of the function y = tan kθ?

What is the period of the cosine function y = cosθ?

What is the effect of p on the graph of y = cos(θ + p)?

What is the range of the function y = tan kθ?

What is the effect of p on the graph of y = tan(θ + p)?

What is the maximum turning point of the cosine function y = cosθ?

What is the y-intercept of the cosine function y = cosθ?

What is the x-intercept of the graph of y = tan kθ?

What is the y-intercept of the graph of y = tan kθ?

What is the effect of a horizontal shift on the graph of y = a(x + p)^2 + q?

What is the shape of the graph of y = a(x + p)^2 + q when a = 1 and q < 0?

What happens to the graph of y = ax^2 + q when a becomes smaller?

What is the turning point of the graph of y = ax^2 + q when a < 0 and q > 0?

What is the effect of p on the axis of symmetry of the graph of y = a(x + p)^2 + q?

What happens to the graph of y = ax^2 + q when q becomes larger?

What is the shape of the graph of y = a(x + p)^2 + q when a < 0 and q > 0?

What happens to the graph of y = ax^2 + q when a becomes larger?

What is the domain of a quadratic function?

What is the range of the function y = a(x + p)^2 + q, if a > 0?

What is the turning point of the graph of y = a(x + p)^2 + q?

What is the effect of a horizontal shift of m units to the right on the graph of y = ax^2 + bx + c?

What is the average gradient of a curve between two points A(x_A, y_A) and C(x_C, y_C)?

What is the vertical asymptote of the hyperbolic function y = a/(x + p) + q?

What is the effect of a on the shape of the graph of y = a/(x + p) + q?

What is the equation of the axis of symmetry of the graph of y = a(x + p)^2 + q?

How do you find the x-intercept of a quadratic function?

What is the effect of a horizontal shift of n units upwards on the graph of y = a(x + p)^2 + q?

What is the period of the sine function y = sin kθ?

What is the effect of a on the amplitude of the sine function y = a sin θ?

What is the y-intercept of the sine function y = sin θ?

What is the effect of q on the graph of y = a sin θ + q?

What is the range of the sine function y = sin θ?

What is the period of the cosine function y = cos kθ?

What is the effect of a on the shape of the graph of y = a cos θ?

What is the x-intercept of the cosine function y = cos θ?

What is the effect of p on the graph of y = cos(θ + p)?

What is the maximum turning point of the cosine function y = cos θ?

What is the period of the function y = tanθ?

What is the effect of a on the shape of the graph of y = a tanθ?

What is the effect of k on the period of the function y = tan kθ?

What is the domain of the function y = tan kθ?