Question

Which statement describes the behavior of the function f (x) = StartFraction 2 x Over 1 minus x squared EndFraction?
The graph approaches –2 as x approaches infinity.
The graph approaches 0 as x approaches infinity.
The graph approaches 1 as x approaches infinity.
The graph approaches 2 as x approaches infinity.

Answer 1

The graph approaches 0 as x → ∞.

Reason: divide numerator and denominator by x^2: f(x) = (2/x)/(1/x^2 − 1). As x → ∞, 2/x → 0 and 1/x^2 − 1 → −1, so the limit is 0/(−1) = 0.