Question

Which functions have removable discontinuities (holes)? Check all of the boxes that apply.

Answer 1

Answer:

a b d

Step-by-step explanation:

Answer 2

Answer:

Option A,B,D

Step-by-step explanation:

For f(x) = (x-1)/(x²-1)

f(x) = (x-1)/(x-1)(x+1)

Therefore hole at x = 1

For f(x) = (x²-9)/(x²+7x+12) = (x-3)(x+3)/(x²+4x+3x+12) = (x-3)(x+3)/(x+3)(x+4)

Common factor (x+3) in numerator and denominator so

Function has hole at x = -3

For f(x) = (x² + 4x + 4)/(x² + 2x - 8) = (x+2)²/(x² +4x -2x -8) = (x+2)²/(x+4)(x-2)

This function has no discontinuity.

For f(x) = (x +7)/(x²+5x-14) = (x+7)/(x² + 7x -2x -14) = (x+7)/(x-2)(x+7)

This function has a hole at x = -7

Option A,B,D have the removable discontinuity.