Question

How do you find asymptotes, local extrema, and points of inflection, given `f(x) = (x^2 - 8)/(x+3)`?

Answer 1

Have a look:

The inflection or change of concavity occurs at the point of discontinuity.

graph{(x^2-8)/(x+3) [-41.1, 41.13, -20.54, 20.55]}

Answer 2

If you also want the slant asymptote, do the division:

`(x^2 - 8)/(x+3) =x-3+1/(x+3)`.

So the line `y=x-3` is a slant asymptote.

That is, as `xrarroo`, the difference between `f(x)` and the line `y=x-3` approaches `0`. (And the same as `xrarr -oo`,)

Slant asymptotes are also called oblique asymptotes.