Question

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

Answer 1

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]}