Question

Determine the values of x on which the function f(x)=2x^2-x-15/4x^2-12x is discontinuous and verify the type of discontinuity at each point.

A.There is a vertical asymptote at 0 and a hole at 3.
B.There are vertical asymptotes at -5/2 & 0 and a hole at 3.
C.There is a vertical asymptote at 3 and a hole at 0.
D.There are vertical asymptotes at 0 & 3

Answer 1

We factor the function

f(x)= [ (2x + 5)(x-3) ]/[ 4x(x-3) ], x ≠ 3

f(x)= [ (2x + 5) ]/[ 4x ], x ≠ 3

A full cancellation of a denominator factor means that there will be a hole. The answer is that there is a vertical asymptote at 0 and a hole at 3.

Explanation:

Answer 2

We factor the function
f(x)= [ (2x + 5)(x-3) ]/[ 4x(x-3) ], x ≠ 3
f(x)= [ (2x + 5) ]/[ 4x ], x ≠ 3
A full cancellation of a denominator factor means that there will be a hole. The answer is that there is a vertical asymptote at 0 and a hole at 3.