select all that are x - intercepts of the tangent graph. \nπ/4 \nπ/2 \nπ \n3π/2 \n3π \ndone \nselect all…

select all that are x - intercepts of the tangent graph. \nπ/4 \nπ/2 \nπ \n3π/2 \n3π \ndone \nselect all that are asymptotes of the tangent graph. \nx = π/4 \nx = π/2 \nx = π \nx = 3π/2 \nx = 3π \ndone

select all that are x - intercepts of the tangent graph. \nπ/4 \nπ/2 \nπ \n3π/2 \n3π \ndone \nselect all that are asymptotes of the tangent graph. \nx = π/4 \nx = π/2 \nx = π \nx = 3π/2 \nx = 3π \ndone

Answer

Explanation:

Step1: Recall x - intercepts of tangent function

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 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). But (\frac{\pi}{4}), (\frac{\pi}{2}), (\frac{3\pi}{2}) do not make (\sin(x)=0).

Step2: Recall asymptotes of tangent function

The tangent function (y=\tan(x)=\frac{\sin(x)}{\cos(x)}) has 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}). (x=\frac{\pi}{4}), (x=\pi), (x = 3\pi) do not make (\cos(x)=0).

Answer:

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