Compare and contrast the points of discontinuity of the following rational functions. f(x)=(x+2)(x−3)/x+2 g(x)=(x+2)(x−3)/x(x+2)

Question

a. Describe at least one similarity between the points of discontinuity.

b. Describe at least one difference between the points of discontinuity.

Answer 1

The factor x + 2 can be canceled making x = -2 a hole (removable discontinuity) for each function.

The function g(x) has the vertical asymptote (infinite discontinuity) at x = 0 because x is a factor in the denominator.