Question

What is the graph of the function `f(x) = (x^2 + 4x-12)/(x+6)`?

Answer 1

Same as `y=x-2`, except a point `x=-6`, where function is undefined.

Explanation:

graph{(x^2 +4x -12)/(x+6) [-10, 10, -10, 10]}

Obviously, the function is undefined at `x=-6` since its denominator would be equal to zero in this case.

In all other cases we can do a simple transformation:
Since `x^2+4x-12 = (x+6)(x-2)`,
`(x^2+4x-12)/(x+6) = x-2`
for all `x != -6`

Therefore, our graph would be identical to the one of `y=x-2`, except in one point `x=-6`, where function is undefined, and which should be excluded from the graph.