# Chapter 2 - Review - Concept Check: 6

(a) This function does not have any asymptotes. (b) This function does not have any asymptotes. (c) This function has vertical asymptotes for $x=(2m-1)\pi/2$ where $m$ is an integer. Here the function always goes to $+\infty$ from the left and to $-\infty$ to the right. (d) This function has two horizontal asymptotes: $y=\pi/2$ when $x$ goes to $+\infty$ and $y=-\pi/2$ when $x$ goes to $-\infty$. (e) This function has the horizontal asymptote $y=0$ when $x$ goes to $-\infty$. (f) This function has the vertical asymptote $x=0$ and it goes to $-\infty$ when $x$ approaches from the right. (g) This function has a vertical asymptote $x=0$ and a horizontal asymptote $y=0$. The function goes to $-\infty$ from the left and $+\infty$ from the right. (h) This function has no asymptotes.

#### Work Step by Step

(a) This function does not have any asymptotes. (b) This function does not have any asymptotes. (c) This function has vertical asymptotes for $x=(2m-1)\pi/2$ where $m$ is an integer. Here the function always goes to $+\infty$ from the left and to $-\infty$ to the right. (d) This function has two horizontal asymptotes: $y=\pi/2$ when $x$ goes to $+\infty$ and $y=-\pi/2$ when $x$ goes to $-\infty$. (e) This function has the horizontal asymptote $y=0$ when $x$ goes to $-\infty$. (f) This function has the vertical asymptote $x=0$ and it goes to $-\infty$ when $x$ approaches from the right. (g) This function has a vertical asymptote $x=0$ and a horizontal asymptote $y=0$. The function goes to $-\infty$ from the left and $+\infty$ from the right. (h) This function has no asymptotes.

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