Question

f(x-2)(x+1) / x+1
Which statements describe the end behavior of the graph of the function shown? Check all that apply.

As x → ∞, y → 1.
As x → ∞, y → ∞.
As x → ∞, y → –∞.
As x → –∞, y → 1.
As x → –∞, y → ∞.
As x → –∞, y → –∞.

Answer 1

Interpret the function as f(x) = (x−2)(x+1)/(x+1). Cancel (x+1) (except at x = −1), so f(x) = x−2 for all x ≠ −1.

Thus as x → ∞, f(x) → ∞, and as x → −∞, f(x) → −∞. (There is a removable hole at x = −1, but that does not change the end behavior.)

Correct choices:
- As x → ∞, y → ∞.
- As x → −∞, y → −∞.