Question

Which of the following rational functions is graphed below?

10
-10
10
-10
O FX-6-53
1
A. F(X) =
(x - 5)
B. F(X) =
-5x
OCAM
C. F(X) =
5x
D. F(x) =
1
(x+5)

Answer 1

D. F(x) = 1/(x +5)²

Explanation:

The vertical asymptote at x=-5 tells you that x=-5 will be a zero of the denominator. The only equation with a denominator factor of (x+5) is ...

F(x) = 1/(x +5)²

_____

Additional comment

The fact that the value of F(x) does not change sign at the vertical asymptote tells you the denominator factor will be of even degree. That is taken for granted here, as all denominators are squares in the answer choices.