select all that are x - intercepts of the tangent graph.\n$\frac{pi}{4}$\n$\frac{pi}{2}$\n$pi$\n$\frac{3pi}{2…

select all that are x - intercepts of the tangent graph.\n$\frac{pi}{4}$\n$\frac{pi}{2}$\n$pi$\n$\frac{3pi}{2}$\n$3pi$\ndone\nselect all that are asymptotes of the tangent graph.\n$x = \frac{pi}{4}$\n$x=\frac{pi}{2}$\n$x=pi$\n$x=\frac{3pi}{2}$\n$x = 3pi$\ndone

select all that are x - intercepts of the tangent graph.\n$\frac{pi}{4}$\n$\frac{pi}{2}$\n$pi$\n$\frac{3pi}{2}$\n$3pi$\ndone\nselect all that are asymptotes of the tangent graph.\n$x = \frac{pi}{4}$\n$x=\frac{pi}{2}$\n$x=pi$\n$x=\frac{3pi}{2}$\n$x = 3pi$\ndone

Answer

Explanation:

Step1: Recall x - intercept property of tangent function

The tangent function (y = \tan(x)=\frac{\sin(x)}{\cos(x)}). The x - intercepts occur when (\sin(x)=0) and (\cos(x)\neq0). The solutions of (\sin(x) = 0) are (x = k\pi), where (k\in\mathbb{Z}). When (k = 0), (x = 0); when (k = 1), (x=\pi); when (k = 3), (x = 3\pi).

Step2: Recall asymptote property of tangent function

The tangent function (y=\tan(x)) has vertical asymptotes when (\cos(x)=0). The solutions of (\cos(x)=0) are (x=\frac{\pi}{2}+k\pi), (k\in\mathbb{Z}). When (k = 0), (x=\frac{\pi}{2}); when (k = 1), (x=\frac{3\pi}{2}).

Answer:

x - intercepts of the tangent graph: (\pi), (3\pi) asymptotes of the tangent graph: (x=\frac{\pi}{2}), (x=\frac{3\pi}{2})