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 tangent - function properties

The tangent function is (y = \tan(x)=\frac{\sin(x)}{\cos(x)}). The (x) - intercepts occur when (\sin(x)=0) and (\cos(x)\neq0). The asymptotes occur when (\cos(x) = 0).

Step2: Find (x) - intercepts

We know that (\sin(x)=0) when (x = k\pi), where (k\in\mathbb{Z}). Among the given options, when (x=\pi) and (x = 3\pi), (\sin(x)=0) and (\cos(x)\neq0).

Step3: Find asymptotes

We know that (\cos(x)=0) when (x=(2k + 1)\frac{\pi}{2}), where (k\in\mathbb{Z}). Among the given options, when (x=\frac{\pi}{2}) and (x=\frac{3\pi}{2}), (\cos(x)=0).

Answer:

(x) - intercepts: (\pi), (3\pi) Asymptotes: (x=\frac{\pi}{2}), (x=\frac{3\pi}{2})