Gr 11 Math Ch 5: The Tangent Function
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Questions and Answers

What is the domain of one branch of the function y = tan(kθ)?

  • θ ∈ (-90°/k, 90°/k) (correct)
  • θ ∈ ℝ
  • θ ∈ (-∞, -90°/k) ∪ (90°/k, ∞)
  • θ ∈ (-90°, 90°)

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

  • (-∞, ∞) (correct)
  • (-1, 1)
  • (0, ∞)
  • [0, ∞)

    • How do you find the x-intercepts of the function y = tan(kθ)?

  • By setting k = 1 and solving for y
  • By setting k = 0 and solving for θ
  • By setting θ = 0 and solving for y
  • By setting y = 0 and solving for θ (correct)

    • What is the y-intercept of the function y = tan(kθ)?

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

    What happens to the graph of the tangent function when p > 0 in y = tan(θ + p)?

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

    What are the asymptotes of the function y = tan(kθ)?

    <p>θ = -90°/k and θ = 90°/k</p> Signup and view all the answers

    What is the period of the function y = tan θ?

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

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

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

    What is the effect of q > 0 on the graph of y = a tan θ + q?

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

    What is the effect of a < 0 on the graph of y = a tan θ?

    <p>The graph is reflected about the x-axis.</p> Signup and view all the answers

    What is the period of the function y = tan 2θ?

    <p>180°/2</p> Signup and view all the answers

    What is the effect of k > 1 on the period of the function y = tan kθ?

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

    What is the effect of k < -1 on the period of the function y = tan kθ?

    <p>The period decreases and the graph is reflected about the y-axis.</p> Signup and view all the answers

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

    <p>(0°, 0), (180°, 0), (360°, 0)</p> Signup and view all the answers

    What is the period of the function y = tan(3θ)?

    <p>60°</p> Signup and view all the answers

    What is the effect of a > 1 on the graph of y = a tan(θ) + q?

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

    What is the effect of q < 0 on the graph of y = a tan(θ) + q?

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

    What is the period of the function y = tan(2θ) + 3?

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

    What is the effect of k < 0 on the graph of y = tan(kθ)?

    <p>The graph is reflected about the y-axis and the period increases.</p> Signup and view all the answers

    What is the effect of a < -1 on the graph of y = a tan(θ) + q?

    <p>The graph is reflected about the x-axis and the branches are steeper.</p> Signup and view all the answers

    What is the effect of k > 0 on the graph of y = tan(kθ)?

    <p>The period decreases and the graph is not reflected.</p> Signup and view all the answers

    What is the period of the function y = tan(-θ)?

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

    What happens to the graph of the function y = tan(kθ) when k > 1?

    <p>The graph of the function compresses horizontally.</p> Signup and view all the answers

    What is the relationship between the value of p and the horizontal shift of the graph of the function y = tan(θ + p)?

    <p>When p &gt; 0, the graph shifts to the left and when p &lt; 0, the graph shifts to the right.</p> Signup and view all the answers

    What is the effect of a tangent function on the angle θ?

    <p>It doubles the angle θ.</p> Signup and view all the answers

    What happens to the asymptotes of the function y = tan(kθ) when k > 1?

    <p>The asymptotes of the function move closer together.</p> Signup and view all the answers

    What is the relationship between the value of k and the period of the function y = tan(kθ)?

    <p>The period of the function is inversely proportional to the value of k.</p> Signup and view all the answers

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

    <p>The graph of the function shifts to the left.</p> Signup and view all the answers

    What happens to the graph of the tangent function when p < 0 in y = tan(θ + p)?

    <p>It shifts to the right by p</p> Signup and view all the answers

    What is the value of kθ that makes the tangent function undefined?

    <p>kθ = 90°</p> Signup and view all the answers

    What is the x-coordinate of the y-intercept of the function y = tan(kθ)?

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

    What is the relationship between the graph of y = tan(kθ) and the graph of y = tan(θ)?

    <p>The graph of y = tan(kθ) is a horizontal compression of the graph of y = tan(θ)</p> Signup and view all the answers

    What is the value of θ that makes the tangent function equal to 0?

    <p>θ = 0°</p> Signup and view all the answers

    What is the period of the function y = tan(4θ)?

    <p>45°</p> Signup and view all the answers

    What is the effect of a = 2 on the graph of the function y = a tan(θ)?

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

    What is the effect of q = 2 on the graph of the function y = tan(θ) + q?

    <p>The graph is shifted vertically upwards by 2 units.</p> Signup and view all the answers

    What is the effect of k = -2 on the graph of the function y = tan(kθ)?

    <p>The period of the graph decreases and the graph is reflected about the y-axis.</p> Signup and view all the answers

    What is the effect of a = -1 on the graph of the function y = a tan(θ)?

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

    What is the period of the function y = tan(θ/2)?

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

    What is the effect of a = 0.5 on the graph of the function y = a tan(θ)?

    <p>The branches of the graph are less steep.</p> Signup and view all the answers

    What is the effect of q = -3 on the graph of the function y = tan(θ) + q?

    <p>The graph is shifted vertically downwards by 3 units.</p> Signup and view all the answers

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