Gr 11 Math Ch 5: The Tangent Function

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

θ ∈ (-90°/k, 90°/k)

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

(-∞, ∞)

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

By setting y = 0 and solving for θ

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

(0, 0) 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 Signup and view all the answers

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

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

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

180° Signup and view all the answers

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

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

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

180°/2 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. 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. Signup and view all the answers

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

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

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

60° 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. 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. Signup and view all the answers

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

90° 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. 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. 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. Signup and view all the answers

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

180° 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. 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. Signup and view all the answers

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

It doubles the angle θ. 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. 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. 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. 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 Signup and view all the answers

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

kθ = 90° Signup and view all the answers

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

0° 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 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) Signup and view all the answers

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

θ = 0° Signup and view all the answers

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

45° Signup and view all the answers

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