Question

Use the function given to answer the question.

Information
y equals StartFraction x plus 2 over x plus 9 EndFraction

Question
What is the range of the function?

Answer options with 5 options
A.
all real numbers except negative 2

B.
all real numbers except negative 9

C.
all real numbers except 1

D.
all real numbers except negative 2 and negative 9

E.
all real numbers except negative 2, negative 9, and 1

Answer 1

y = (x+2)/(x+9). Set y = (x+2)/(x+9) and solve for x:

y(x+9) = x+2 → yx + 9y = x + 2 → x(y−1) = 2 − 9y.

If y = 1 this gives 2 = 9 (impossible), so y ≠ 1. For any y ≠ 1, x = (2 − 9y)/(y − 1), and this x is not equal to −9 for any y, so every y ≠ 1 is attained.

Thus the range is all real numbers except 1. Answer: C.