Question

question 4 of 6. step 1 of 2
6/12
correct
graph the following function: y = \frac{3}{2}-3\tan(x)
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 given function $y=\frac{3}{2}-3\tan(x)$ is based on the tangent function $y = \tan(x)$. The tangent - function has vertical asymptotes at $x=(n+\frac{1}{2})\pi$, where $n\in\mathbb{Z}$, and it has a period of $\pi$. Its graph passes through the origin $(0,0)$ and has a characteristic S - shaped curve between consecutive asymptotes.

Answer:

The basic function is the tangent function, and its shape is a curve with vertical asymptotes at $x=(n +\frac{1}{2})\pi,n\in\mathbb{Z}$ and a period of $\pi$.