Question

what is the y - intercept of y = tan x? select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the y - intercept is (type an exact answer, using radicals as needed.) b. there is no y - intercept.

Explanation:

Step1: Recall y - intercept definition

The y - intercept of a function \(y = f(x)\) is found by setting \(x = 0\) and evaluating \(y\).

Step2: Evaluate \(y=\tan x\) at \(x = 0\)

We know that \(\tan x=\frac{\sin x}{\cos x}\). When \(x = 0\), \(\sin(0)=0\) and \(\cos(0)=1\). So \(\tan(0)=\frac{\sin(0)}{\cos(0)}=\frac{0}{1}=0\).

Answer:

A. The y - intercept is \(0\)