Question

How do you graph `f(x)= (x^2-100)/(x+10)`?

Answer 1

`f(x) = (x^2-100)/(x+10) = ((x-10)(x+10))/(x+10) = x-10`

with excluded value `x=-10`.

This is a straight line of slope `1` passing through `(0, -10)` and `(10, 0)` with excluded point `(-10, -20)`

Explanation:

`f(x) = (x^2-100)/(x+10)`

`= ((x-10)(x+10))/(x+10)`

`= x-10`

with exclusion `x!=-10`.

The graph of `f(x)` is like the graph of `x-10` except that `f(x)` is not defined at the point `(-10, -20)`

All the limits as you approach that point behave well, it's just that `f(-10)` is undefined as it's equal to `0/0`.

graph{(x^2-100)/(x+10) [-37.5, 42.5, -24, 16]}