# What are the asymptotes for y=−4/x+2 and how do you graph the function?

What are the asymptotes for $y=-\frac{4}{x+2}$ and how do you graph the function?
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graulhavav9
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 $x\to \infty$, the number will get so small and close to 0, but never reach 0.

The graph is that of $y=\frac{1}{x}$ 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 $y=\frac{1}{x}$
graph{1/x [-10, 10, -5, 5]}

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

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

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