Question

Which statement describes the behavior of the function f (x) = StartFraction 3 x Over 4 minus x EndFraction?
The graph approaches –3 as x approaches infinity.
The graph approaches 0 as x approaches infinity.
The graph approaches 3 as x approaches infinity.
The graph approaches 4 as x approaches infinity.

Answer 1

The first statement. As x → ∞, f(x) = 3x/(4 − x) = 3/(4/x − 1) → 3/(0 − 1) = −3, so the graph approaches −3.