Question

Does the function

f(x) = (3x2 + 2x - 8)/(x2 - 3x - 10) Have a hole in its graph? if so, where does the hole occur?

Answer 1

factor the denominator. set the factored parts equal to zero and then solve for x. Those x's should be the holes. (x^2 - 3x - 10) = (x-5)(x+2), so holes at x = 5 and x = -2

Answer 2

oh wait, factor the top too and if they cancel out, then that part is the hole.

Answer 3

x = -2 is the hole because, the function in the numerator factors into (x+2)(3x-4).

Answer 4

The hole is wherever the denominator is 0, since a denominator cannot be equal to zero, thus creating a "hole."