Question

What are the discontinuities of the function f(x) = (x^2 + 5x + 6)/(2x + 16)?

A. x = -2
B. x = -8
C. x = -5
D. x^2 = 0

Answer 1

The discontinuities of the function f(x) = (x^2 + 5x + 6)/(2x + 16) occur where the denominator is zero, which is at x = -8. There are no other discontinuities, making option B the correct answer.

Step-by-step explanation:

The discontinuities of a function occur where the function is not defined or not continuous. For the function f(x) = (x2 + 5x + 6)/(2x + 16), discontinuities would be the values of x that make the denominator equal to zero since division by zero is undefined. To find these values, we set the denominator equal to zero and solve for x:

2x + 16 = 0

x = -8

Therefore, the function is discontinuous at x = -8, which corresponds to option B. There are no other values of x that make the denominator zero, so there are no other discontinuities.