What are the asymptotes for $y=-4/(x+2)$ and how do you graph the function?

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What are the asymptotes for $y=-4/(x+2)$ and how do you graph the function?

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Answer 1 · 2017-10-13T12:01:13

Asymptotes:
$y=o$
$x=-2$

Explanation:

The asymptotes are at $x=-2$ and $y0$ , this is because when $x=-2$ the denominator would equal $0$ which cannot be solved. The $y=0$ asymptote is caused because as $x->oo$ , the number will get so small and close to 0, but never reach 0.

The graph is that of $y=1/x$ but shifted to the left by 2, and flipped in the x-axis. The curves will be more rounded as the numerator is a larger number.

Graph of $y=1/x$
graph{1/x [-10, 10, -5, 5]}

Graph of $y=4/x$
graph{4/x [-10, 10, -5, 5]}

Graph of $y=-4/x$
graph{-4/x [-10, 10, -5, 5]}

Graph of $y=-4/(x+2)$
graph{-4/(x+2) [-10, 10, -5, 5]}

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What are the asymptotes for $y=-4/(x+2)$ and how do you graph the function?

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What are the asymptotes for $y=-4/(x+2)$ and how do you graph the function?