Gr 11 Math Ch 5: The Tangent Function

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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)?

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

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

The graph shifts to the left by p (B) Signup and view all the answers

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

θ = -90°/k and θ = 90°/k (D) Signup and view all the answers

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

180° (B) Signup and view all the answers

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

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

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

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

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

The graph is reflected about the x-axis. (A) Signup and view all the answers

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

180°/2 (C) Signup and view all the answers

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

The period decreases. (C) Signup and view all the answers

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

The period decreases and the graph is reflected about the y-axis. (B) Signup and view all the answers

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

(0°, 0), (180°, 0), (360°, 0) (C) Signup and view all the answers

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

60° (A) Signup and view all the answers

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

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

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

The graph is shifted vertically downwards by q units. (B) Signup and view all the answers

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

90° (A) Signup and view all the answers

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

The graph is reflected about the y-axis and the period increases. (A) Signup and view all the answers

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

The graph is reflected about the x-axis and the branches are steeper. (D) Signup and view all the answers

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

The period decreases and the graph is not reflected. (D) Signup and view all the answers

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

180° (D) Signup and view all the answers

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

The graph of the function compresses horizontally. (C) 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)?

When p > 0, the graph shifts to the left and when p < 0, the graph shifts to the right. (D) Signup and view all the answers

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

It doubles the angle θ. (B) Signup and view all the answers

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

The asymptotes of the function move closer together. (C) Signup and view all the answers

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

The period of the function is inversely proportional to the value of k. (C) 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)?

The graph of the function shifts to the left. (B) Signup and view all the answers

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

It shifts to the right by p (A) Signup and view all the answers

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

kθ = 90° (B) Signup and view all the answers

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

0° (D) 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 (C) Signup and view all the answers

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

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

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

θ = 0° (C) Signup and view all the answers

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

45° (C) Signup and view all the answers

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

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

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

The graph is shifted vertically upwards by 2 units. (A) Signup and view all the answers

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

The period of the graph decreases and the graph is reflected about the y-axis. (B) Signup and view all the answers

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

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

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

360° (D) Signup and view all the answers

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

The branches of the graph are less steep. (C) Signup and view all the answers

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

The graph is shifted vertically downwards by 3 units. (D) Signup and view all the answers