Question

The graph below shows the function f(x)= 5x+10/x^2+7x+10

Where is the removable discontinuity of f(x) located?


A.x = –5

B.x = 0

C.x = –2

D.x = 5

Answer 1

C. x = -2

Explanation:

A proper graph of the function will have an open circle at (-2, 5/3), so you should be able to read the answer from the graph.

The factorization is ...

... f(x) = 5(x +2)/((x +5)(x +2))

The removable discontinuity is created by the factor (x+2)/(x+2), which is undefined at x = -2.