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

The function simplifies to f(x) = (x-2)(x+1)/(x+1) = x − 2 for x ≠ −1 (there is a removable hole at x = −1). So the graph is a line with slope 1, hence as x → ∞, y → ∞ and as x → −∞, y → −∞.

Select:
- As x → ∞, y → ∞.
- As x → −∞, y → −∞.