Question

How do you prove that the function `f(x)=(x^2+7x+10)/(x+5)` is continuous everywhere but x=-5?

Answer 1

Factor and rewrite the function.

Explanation:

`f(x) = (x^2+7x+10)/(x+5)`

`= ((x+2)(x+5))/(x+5)`

`= x+2` for `x != -5`

Use whatever tools you have developed to show that a linear function is continuous,

but note that `f(-5)` is not defined, so `f` cannot be continuous at `-5`.