Gr 11 Math Ch 5 SUM: Functions
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Questions and Answers

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

  • Change in the shape of the graph
  • Vertical shift
  • Change in the axis of symmetry
  • Horizontal shift (correct)
  • 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 (correct)
  • Minimum turning point below the x-axis
  • Maximum turning point below the x-axis
  • Maximum turning point above the x-axis
  • What happens to the graph of $y = ax^2 + q$ when $a$ becomes larger?

  • The graph becomes wider
  • The graph becomes horizontal
  • The graph remains the same
  • The graph becomes narrower (correct)
  • What is the effect of the parameter $q$ on the graph of $y = a(x + p)^2 + q$?

    <p>Vertical shift (C)</p> Signup and view all the answers

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

    <p>A 'frown' with a maximum turning point (A)</p> Signup and view all the answers

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

    <p>The line $x = -p$ (C)</p> Signup and view all the answers

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

    <p>$q$ (B)</p> Signup and view all the answers

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

    <p>The graph becomes a horizontal line $y = q$ (A)</p> Signup and view all the answers

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

    <p>The graph is shifted horizontally by p units. (A)</p> Signup and view all the answers

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

    <p>x = -p (B)</p> Signup and view all the answers

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

    <p>{y: y &gt; q, y ∈ ℝ} (A)</p> Signup and view all the answers

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

    <p>If a &lt; 0, the graph is reflected about the horizontal asymptote. (A)</p> Signup and view all the answers

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

    <p>The graph is shifted vertically by q units. (B)</p> Signup and view all the answers

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

    <p>y = q (B)</p> Signup and view all the answers

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

    <p>{y: y ≠ q, y ∈ ℝ} (C)</p> Signup and view all the answers

    What is the domain of a quadratic function?

    <p>All real numbers (C)</p> Signup and view all the answers

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

    <p>The graph is shifted horizontally by p units. (A)</p> Signup and view all the answers

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

    <p>All real numbers greater than or equal to the y-coordinate of the vertex (C)</p> Signup and view all the answers

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

    <p>Set y = 0 (D)</p> Signup and view all the answers

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

    <p>The solution to f(x) = 0 (A)</p> 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?

    <p>x = -p (D)</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?

    <p>The graph lies below the horizontal asymptote. (D)</p> Signup and view all the answers

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

    <p>A horizontal shift to the left by m units (D)</p> Signup and view all the answers

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

    <p>The gradient of the line passing through the two points (C)</p> Signup and view all the answers

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

    <p>(f(a + h) - f(a)) / h (B)</p> Signup and view all the answers

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

    <p>A vertical shift by q units (A)</p> Signup and view all the answers

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

    <p>The line y = q (D)</p> 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?

    <p>For a &gt; 0, the graph lies in the first and third quadrants (C)</p> Signup and view all the answers

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

    <p>360° (A)</p> Signup and view all the answers

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

    <p>1 (B)</p> Signup and view all the answers

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

    <p>Vertical shift (B)</p> Signup and view all the answers

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

    <p>The period decreases (C)</p> Signup and view all the answers

    What is the period of the function y = tanθ?

    <p>180° (B)</p> Signup and view all the answers

    What is the domain of the function y = tanθ?

    <p>{θ: 0° ≤ θ ≤ 360°, θ ≠ 90°, 270°} (D)</p> Signup and view all the answers

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

    <p>(270°, 0) (A), (0°, 0) (B), (180°, 0) (C)</p> Signup and view all the answers

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

    <p>a vertically stretches the graph (D)</p> Signup and view all the answers

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

    <p>The amplitude increases (D)</p> Signup and view all the answers

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

    <p>the period is 180°/k (C)</p> Signup and view all the answers

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

    <p>360° (D)</p> Signup and view all the answers

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

    <p>Horizontal shift to the left (C)</p> Signup and view all the answers

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

    <p>{f(θ): f(θ) ∈ ℝ} (B)</p> Signup and view all the answers

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

    <p>p horizontally shifts the graph (C)</p> Signup and view all the answers

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

    <p>(0°, 1) (B)</p> Signup and view all the answers

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

    <p>(0°, 1) (B)</p> Signup and view all the answers

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

    <p>(0°, 0) (A)</p> Signup and view all the answers

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

    <p>(0°, 0) (D)</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?

    <p>A vertical shift occurs (A)</p> 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?

    <p>A smile (B)</p> Signup and view all the answers

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

    <p>The graph becomes wider (A)</p> 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?

    <p>Above the x-axis (A)</p> 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?

    <p>The axis of symmetry is shifted to the right (B)</p> Signup and view all the answers

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

    <p>The graph is shifted vertically upwards (B)</p> 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?

    <p>A frown (B)</p> Signup and view all the answers

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

    <p>The graph becomes narrower (B)</p> Signup and view all the answers

    What is the domain of a quadratic function?

    <p>(-∞, ∞) (D)</p> Signup and view all the answers

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

    <p>[q, ∞) (A)</p> Signup and view all the answers

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

    <p>(p, q) (A)</p> 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?

    <p>Replace x with x - m (A)</p> 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)?

    <p>y_C - y_A / x_C - x_A (C)</p> Signup and view all the answers

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

    <p>x = -p (B)</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?

    <p>It affects the shape and quadrants of the graph (B)</p> 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?

    <p>x = p (B)</p> Signup and view all the answers

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

    <p>Set y = 0 and solve for x (D)</p> 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?

    <p>Replace y with y + n (B)</p> Signup and view all the answers

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

    <p>360°/k (B)</p> Signup and view all the answers

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

    <p>a increases the amplitude (A)</p> Signup and view all the answers

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

    <p>(0°, 0) (D)</p> Signup and view all the answers

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

    <p>q shifts the graph vertically (D)</p> Signup and view all the answers

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

    <p>(-1, 1) (C)</p> Signup and view all the answers

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

    <p>360°/k (A)</p> Signup and view all the answers

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

    <p>a increases the amplitude (C)</p> Signup and view all the answers

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

    <p>(90°, 0) (B), (180°, 0) (C)</p> Signup and view all the answers

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

    <p>p shifts the graph horizontally (D)</p> Signup and view all the answers

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

    <p>(0°, 1) (B), (360°, 1) (D)</p> Signup and view all the answers

    What is the period of the function y = tanθ?

    <p>180° (B)</p> Signup and view all the answers

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

    <p>For a &gt; 1, the branches of the graph are steeper. (C)</p> Signup and view all the answers

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

    <p>The period decreases as k increases. (B)</p> Signup and view all the answers

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

    <p>The set of real numbers such that -90°/k &lt; θ &lt; 90°/k. (C)</p> Signup and view all the answers

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

    <p>The graph is shifted vertically upwards by q units. (A)</p> Signup and view all the answers

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

    <p>All real numbers. (A)</p> Signup and view all the answers

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

    <p>The graph is shifted horizontally by p units. (B)</p> Signup and view all the answers

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

    <p>(0, 0) (A)</p> 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?

    <p>The graph is reflected about the y-axis. (D)</p> Signup and view all the answers

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

    <p>The domain is all real numbers except x = -p. (C)</p> Signup and view all the answers

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

    <p>There is no vertical asymptote. (A)</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?

    <p>The graph is shifted horizontally to the right. (B)</p> Signup and view all the answers

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

    <p>The range is all real numbers greater than q. (D)</p> Signup and view all the answers

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

    <p>The axis of symmetry is the line x = -p. (A)</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?

    <p>The graph is shifted vertically upwards. (B)</p> Signup and view all the answers

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

    <p>The horizontal asymptote is the line y = q. (C)</p> 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?

    <p>The range remains the same. (A)</p> Signup and view all the answers

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

    <p>The x-intercept is the point where y = 0. (D)</p> Signup and view all the answers

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

    <p>The graph is a 'frown' and has a maximum turning point. (D)</p> Signup and view all the answers

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

    <p>The graph is shifted vertically upwards. (C)</p> Signup and view all the answers

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

    <p>The graph becomes narrower. (B)</p> 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?

    <p>The graph is shifted to the left by p units. (C)</p> Signup and view all the answers

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

    <p>The line x = -p. (D)</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?

    <p>The graph becomes wider. (A)</p> Signup and view all the answers

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

    <p>(-p, q). (B)</p> 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?

    <p>The graph is a 'frown' and has a maximum turning point. (B)</p> 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?

    <p>The graph is stretched or compressed. (B)</p> Signup and view all the answers

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

    <p>All real numbers. (D)</p> Signup and view all the answers

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

    <p>The line y = q. (B)</p> 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?

    <p>The graph is shifted horizontally. (B)</p> Signup and view all the answers

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

    <p>All real numbers greater than q. (D)</p> Signup and view all the answers

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

    <p>The line x = -p. (D)</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?

    <p>The graph is shifted vertically. (C)</p> Signup and view all the answers

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

    <p>360° / k (D)</p> Signup and view all the answers

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

    <p>The point (-p, q). (B)</p> 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?

    <p>The graph is stretched or compressed. (D)</p> Signup and view all the answers

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

    <p>The amplitude is multiplied by a (B)</p> Signup and view all the answers

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

    <p>[-1, 1] (B)</p> Signup and view all the answers

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

    <p>The point (0, q). (D)</p> Signup and view all the answers

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

    <p>The graph shifts to the left by p units (D)</p> Signup and view all the answers

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

    <p>The amplitude is multiplied by a and the graph is unaffected (C)</p> Signup and view all the answers

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

    <p>(0°, 1) (D)</p> Signup and view all the answers

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

    <p>360° / k (D)</p> Signup and view all the answers

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

    <p>The graph shifts to the left by p units (C)</p> Signup and view all the answers

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

    <p>{θ : θ ∈ ℝ} (C)</p> Signup and view all the answers

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

    <p>(180°, 0) (B)</p> Signup and view all the answers

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

    <p>Set y = 0 and solve for x. (D)</p> Signup and view all the answers

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

    <p>x = 0 (B)</p> Signup and view all the answers

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

    <p>Replace x with x - m in the equation. (C)</p> Signup and view all the answers

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

    <p>gradient = (y2 - y1) / (x2 - x1) (B)</p> 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?

    <p>For a &gt; 0, the graph lies in the first and third quadrants. (C)</p> Signup and view all the answers

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

    <p>Set x = 0 and solve for y. (D)</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?

    <p>The graph is shifted horizontally by p units. (A)</p> Signup and view all the answers

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

    <p>The vertical line x = -p. (D)</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))?

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

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

    <p>The graph is shifted vertically by q units. (A)</p> Signup and view all the answers

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

    <p>180° (B)</p> Signup and view all the answers

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

    <p>Vertical shift (D)</p> Signup and view all the answers

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

    <p>θ ≠ 90°/k, 270°/k (D)</p> Signup and view all the answers

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

    <p>The period decreases (A)</p> Signup and view all the answers

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

    <p>The branches of the graph are steeper (A)</p> Signup and view all the answers

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

    <p>Horizontal shift (B)</p> Signup and view all the answers

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

    <p>(0, 0) (A)</p> Signup and view all the answers

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

    <p>All real values of y (C)</p> Signup and view all the answers

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

    <p>The amplitude increases (A)</p> Signup and view all the answers

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

    <p>The period decreases (A)</p> Signup and view all the answers

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

    <p>(0, 0) (C)</p> Signup and view all the answers

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

    <p>The graph shifts horizontally to the left (A)</p> Signup and view all the answers

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

    <p>[-1, 1] (A)</p> Signup and view all the answers

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

    <p>The amplitude increases (D)</p> Signup and view all the answers

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

    <p>(90, 0) (A)</p> Signup and view all the answers

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

    <p>360°/k (C)</p> Signup and view all the answers

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

    <p>The graph shifts vertically upwards (A)</p> Signup and view all the answers

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

    <p>(90, 1) (A)</p> Signup and view all the answers

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

    <p>The branches of the graph are steeper. (D)</p> Signup and view all the answers

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

    <p>180°/k (D)</p> Signup and view all the answers

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

    <p>A horizontal shift occur. (D)</p> Signup and view all the answers

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

    <p>(-∞, ∞) (A)</p> Signup and view all the answers

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

    <p>{θ : -90°/k &lt; θ &lt; 90°/k, θ ∈ ℝ} (D)</p> Signup and view all the answers

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

    <p>The period decreases. (D)</p> Signup and view all the answers

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

    <p>0° (A)</p> Signup and view all the answers

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

    <p>0 (D)</p> Signup and view all the answers

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

    <p>A change in shape and quadrants (A)</p> Signup and view all the answers

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

    <p>{ $y : y &lt; q, y \in \mathbb{R} $} (D)</p> Signup and view all the answers

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

    <p>Horizontal shift to the left by m units. (D)</p> Signup and view all the answers

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

    <p>The line $x = -p$ (B)</p> Signup and view all the answers

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

    <p>The vertical line x = -p. (D)</p> Signup and view all the answers

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

    <p>The graph moves closer to the axes (A)</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?

    <p>A larger value of a increases the steepness of the graph. (A)</p> Signup and view all the answers

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

    <p>A horizontal shift (D)</p> Signup and view all the answers

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

    <p>The gradient of the line passing through points A and C. (D)</p> Signup and view all the answers

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

    <p>The line $y = q$ (D)</p> Signup and view all the answers

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

    <p>{ $x : x eq -p, x \in \mathbb{R} $} (D)</p> Signup and view all the answers

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

    <p>A larger value of q shifts the graph vertically upwards. (B)</p> Signup and view all the answers

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

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

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

    <p>A vertical shift (A)</p> Signup and view all the answers

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

    <p>The line y = q. (A)</p> Signup and view all the answers

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

    <p>The line $y = q$ (D)</p> Signup and view all the answers

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

    <p>A change in shape and quadrants (C)</p> 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?

    <p>A positive value of a results in a graph in the first and third quadrants. (D)</p> Signup and view all the answers

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

    <p>The line x = -p. (A)</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?

    <p>The graph is shifted horizontally to the left by p units. (B)</p> Signup and view all the answers

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

    <p>It changes the graph from a 'smile' to a 'frown' (B)</p> Signup and view all the answers

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

    <p>2 units to the left (D)</p> Signup and view all the answers

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

    <p>3 units upwards (D)</p> Signup and view all the answers

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

    <p>It shifts the graph vertically upwards (B)</p> Signup and view all the answers

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

    <p>x = -p (C)</p> Signup and view all the answers

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

    <p>The graph becomes wider (A)</p> Signup and view all the answers

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

    <p>A minimum point below the x-axis (D)</p> Signup and view all the answers

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

    <p>It shifts the graph horizontally (C)</p> Signup and view all the answers

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

    <p>A horizontal shift only. (B)</p> Signup and view all the answers

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

    <p>x = -p (D)</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?

    <p>A vertical shift only. (B)</p> Signup and view all the answers

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

    <p>All real numbers except q (A)</p> Signup and view all the answers

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

    <p>A reflection about the horizontal asymptote. (B)</p> Signup and view all the answers

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

    <p>y = q (A)</p> Signup and view all the answers

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

    <p>All real numbers except -p (C)</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?

    <p>A horizontal shift only. (A)</p> Signup and view all the answers

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

    <p>The line x = -p (B)</p> Signup and view all the answers

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

    <p>All real numbers except q (A)</p> Signup and view all the answers

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

    <p>The graph becomes steeper and curves less (C)</p> Signup and view all the answers

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

    <p>90° (D)</p> Signup and view all the answers

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

    <p>The lines θ = 90° and θ = 270° (B)</p> Signup and view all the answers

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

    <p>The graph shifts horizontally to the right by p units (B)</p> Signup and view all the answers

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

    <p>{θ : 0° ≤ θ ≤ 360°, θ ≠ 90°, 270°} (A)</p> Signup and view all the answers

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

    <p>{f(θ) : f(θ) ∈ ℝ} (C)</p> Signup and view all the answers

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

    <p>(0°, 0) (C)</p> Signup and view all the answers

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

    <p>The period decreases as k increases (A)</p> 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)?

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

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

    <p>The period is divided by $|k|$ (A)</p> 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?

    <p>For a &gt; 0, the graph lies in the first and third quadrants. (D)</p> Signup and view all the answers

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

    <p>$[q-1, q+1]$ (B)</p> 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?

    <p>The axis of symmetry is the line x = -p. (C)</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?

    <p>The graph is shifted horizontally to the right by p units. (A)</p> Signup and view all the answers

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

    <p>The amplitude is multiplied by $a$ (D)</p> Signup and view all the answers

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

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

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

    <p>$(0^\circ, 1)$ (C)</p> 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?

    <p>For q &gt; 0, the graph is shifted vertically upwards by q units. (B)</p> Signup and view all the answers

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

    <p>The graph is shifted horizontally by $p$ units (D)</p> Signup and view all the answers

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

    <p>$\frac{360^\circ}{|k|}$ (B)</p> Signup and view all the answers

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

    <p>The domain is all real numbers. (A)</p> Signup and view all the answers

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

    <p>${ heta : heta \in \mathbb{R} }$ (D)</p> 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?

    <p>For a &gt; 0, the graph opens upwards. (B)</p> Signup and view all the answers

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

    <p>$(180^\circ, 0)$ (B), $(360^\circ, 0)$ (C), $(0^\circ, 0)$ (D)</p> Signup and view all the answers

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

    <p>The range is all real numbers greater than or equal to q. (B)</p> 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?

    <p>The axis of symmetry is the line x = p. (D)</p> Signup and view all the answers

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

    <p>The amplitude of the graph is multiplied by $a$ (D)</p> Signup and view all the answers

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

    <p>$(180^\circ, -1)$ (C)</p> 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?

    <p>The graph is a &quot;frown&quot; and has a maximum turning point. (C)</p> 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?

    <p>The graph is shifted to the left by $p$ units. (A)</p> 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?

    <p>The line $x = -p$. (A)</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?

    <p>The graph becomes wider and the turning point is below the x-axis. (D)</p> 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?

    <p>The graph is shifted to the right by $p$ units. (D)</p> 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?

    <p>The point $(0, q)$. (A)</p> 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?

    <p>The graph becomes narrower and the turning point is to the left of the y-axis. (B)</p> 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?

    <p>The graph is shifted vertically downwards. (C)</p> Signup and view all the answers

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

    <p>The period of the function is 180°/|k| (A)</p> Signup and view all the answers

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

    <p>The domain of the function is the set of all real numbers except θ = 90° and θ = 270° (B)</p> Signup and view all the answers

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

    <p>For a &gt; 1, the branches of the graph are steeper (A)</p> Signup and view all the answers

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

    <p>For q &gt; 0, the graph is shifted vertically upwards by q units (B)</p> Signup and view all the answers

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

    <p>θ = 90° (B), θ = 270° (D)</p> Signup and view all the answers

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

    <p>(0°, 0) (A), (180°, 0) (B), (270°, 0) (D)</p> Signup and view all the answers

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

    <p>For p &gt; 0, the graph is shifted horizontally to the left by p units (C)</p> Signup and view all the answers

    What is the period of the function y = tanθ?

    <p>The period of the function is 180° (C)</p> Signup and view all the answers

    What is the range of the function y = tanθ?

    <p>The range of the function is the set of all real numbers (A)</p> Signup and view all the answers

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

    <p>For a &gt; 0, the y-intercept is (0, 0) (D)</p> Signup and view all the answers

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