Question

(c) Does f (x) have any holes? If so, where are they? (just the x-coordinate is suffi- cient)(d) Does f (x) have any x-intercepts? If so, what are they?

Answer 1

$f(x)=\frac{2(x+7)(x-3)^2(x+1)}{3(x-4)^3(x+5)(x+1)}$

f(x) is not defined where the term of the denominator is zero.

This happens when x = 4, x = -5 or x = -1

The x-intercepts is the points where f(x) = 0

this happens when x = -7 and x = 3

Notice that x = -1 can't be a x-intercept because the function is not defined at this point.