which of the graphs below is the correct graph of y = tan(x)? graph a graph b graph c graph d a graph a b…

Answer:

C. Graph C

Explanation:

Step1: Recall tangent - function properties

The function (y = \tan(x)) has vertical asymptotes at (x=\frac{\pi}{2}+n\pi), (n\in\mathbb{Z}), and it passes through the origin ((0,0)) since (\tan(0)=\frac{\sin(0)}{\cos(0)} = 0).

Step2: Analyze Graph A

Graph A does not pass through the origin, so it cannot be the graph of (y = \tan(x)).

Step3: Analyze Graph B

Graph B does not pass through the origin, so it cannot be the graph of (y=\tan(x)).

Step4: Analyze Graph C

Graph C has vertical asymptotes at (x = \frac{\pi}{2}+n\pi) and passes through the origin, which are the key characteristics of (y=\tan(x)).

Step5: Analyze Graph D

Graph D has incorrect behavior near the origin and does not match the shape of the tangent - function graph.