GRAPHING TANGENT FUNCTIONS WITH TRANSFORMATIONS WORKSHEET

Answer Key

1)  

• Thus two consecutive asymptotes occur at x = -𝜋 and x = 𝜋.
• An x-intercept is 0 and the graph passes through (0, 0).
• So, the required points on the curve are (-𝜋/2, -2) and (𝜋/2, 2).

x = 𝜋(2k + 1)

• When k = -1, x = -𝜋
• When k = 0, x = 𝜋
• When k = 1, x = 3𝜋
• When k = 2, x = 5𝜋

2)  

• Thus two consecutive asymptotes occur at x = -3𝜋/4 and x = 𝜋/4.
• x-intercept is at (-𝜋/4, 0)
• the required points are (-𝜋/2, -1) and (0, 1).

x = 𝜋(k + 1/4)

• When k = -1, x = -3𝜋/4
• When k = 0, x = 𝜋/4
• When k = 1, x = 5𝜋/4
• When k = 2, x = 9𝜋/4

3)  

• Thus two consecutive asymptotes occur at x = -2𝜋 and x = 2𝜋.
• x-intercept is at (0, 0) at the interval (-2𝜋, 2𝜋).

• the required points are (-𝜋, -3) and (𝜋, 3).

x = 2𝜋(2k + 1)

• When k = -1, x = -3𝜋/4
• When k = 0, x = 𝜋/4
• When k = 1, x = 5𝜋/4
• When k = 2, x = 9𝜋/4

4)  

• Thus two consecutive asymptotes occur at x = -𝜋/4 and x = 𝜋/4.
• x-intercept is at 0
• the required points are (-𝜋/8, -0.5) and (𝜋/8, 0.5).

x = (1/4)𝜋(2k + 1)

• When k = -1, x = -𝜋/4
• When k = 0, x = 𝜋/4
• When k = 1, x = 3𝜋/4
• When k = 2, x = 5𝜋/4

5)  

• Thus two consecutive asymptotes occur at x = -𝜋 and x = 𝜋.
• x-intercept is 0
• the required points are (-𝜋/2, -2) and (𝜋/2, 2).

x = 𝜋(2k + 1)

• When k = -1, x = -𝜋
• When k = 0, x = 𝜋
• When k = 1, x = 3𝜋
• When k = 2, x = 5𝜋