Question

How do you find the domain, identify any horizontal, vertical, and slant (if possible) asymptotes and identify holes, x-intercepts, and y-intercepts for `(x^2-25)/(x^2+5x)`?

Answer 1

I'll give you only a partial answer:

The function can be rewritten as:

`=((x-5)(x+5))/(x*(x+5))`

We can cancel out the `(x+5)`'s
BUT this we only do if `x!=-5`
Also `x!=0`
(both cases will make the numerator `=0`)
So `x=0andx=-5`are points of interest.

The function turns into:
`=(x-5)/x`

That (if `x` gets large enough) will converge to `x/x=1`
graph{(x^2-25)/(x^2+5x) [-22.82, 22.81, -11.4, 11.42]}