Find where equation is discontinuous

Question

Where is  discontinuous?

Question options:

1)	f(x) is continuous everywhere
2)	1
3)	1, 4
4)	4

Answer 1

If you factor the denominator, this will find the points of discontinuity of a rational function.

x²-5x+4 Factor

(x-1)(x-4) Set factors equal to zero and solve

x-1=0

x=1 (This is a hole, because this factor matches what is in the numerator)

x-4=0

x=4 (This is a vertical asymptote)

The answer is 3