Precalculus: Graph the Tan function

Question

Graph the function.

y = tan(1/4 𝑥) + 1

Answer 1

Hi Katelyn A.,

For y = tan(x/4) + 1, you have a period change of π/(1/4) = 4π, and a vertical shift of 1.

Your vertical asymptotes are at 2π + 4πk (k is an integer).

To Graph:

For two periods, graph vertical asymptotes at x = -2π, 2π, 6π.

Make center line y = 1.

Plot points (-π, 0); (0, 1); (π, 2), connect these points between the vertical asymptotes to complete one period of tan(x/4) + 1.

Plot points (3π, 0); (4π, 1); (5π, 2), for the second period.

I hope this helps, Joe.