Question

graph the following function: y = -\frac{3}{2}-\frac{5}{2}\tan(\frac{4}{5}x - 2\pi)
step 1 of 2: identify the shape of the more basic function that has been shifted, reflected, stretched or compressed.

Explanation:

Step1: Recall basic trigonometric functions

The basic function related to the given function $y =-\frac{3}{2}-\frac{5}{2}\tan(\frac{4}{5}x - 2\pi)$ is the tangent function $y = \tan(x)$. The general form of a tangent - type function is $y = A\tan(Bx - C)+D$. Here, the basic function before any transformations is $y=\tan(x)$.

Answer:

The tangent function $y = \tan(x)$