which function is graphed?\n$y = 3\\cot(x)+2$\n$y = 3\\cot(x + 3)$\n$y = 3\\tan(x)+2$\n$y = 3\\tan(x +…

which function is graphed?\n$y = 3\\cot(x)+2$\n$y = 3\\cot(x + 3)$\n$y = 3\\tan(x)+2$\n$y = 3\\tan(x + 2)$\ndone

which function is graphed?\n$y = 3\\cot(x)+2$\n$y = 3\\cot(x + 3)$\n$y = 3\\tan(x)+2$\n$y = 3\\tan(x + 2)$\ndone

Answer

Answer:

C. $y = 3\tan(x)+2$

Explanation:

Step1: Recall cotangent and tangent shapes

Cotangent has vertical asymptotes at $x = n\pi$ and tangent at $x=(n +\frac{1}{2})\pi$, $n\in\mathbb{Z}$. The graph has asymptotes at $x=(n+\frac{1}{2})\pi$, so it's a tangent - type function.

Step2: Consider vertical shift

The general form of a tangent function is $y = A\tan(Bx - C)+D$. The graph is shifted up 2 units. For $y = 3\tan(x)+2$, $A = 3$, $B = 1$, $C = 0$, $D=2$ which matches the graph's vertical shift and shape.