which graph represents the function $f(x)=(\frac{3}{2})^{-x}$
which graph represents the function $f(x)=(\frac{3}{2})^{-x}$
Answer
Explanation:
Step1: Rewrite the function
We know that (f(x)=(\frac{3}{2})^{-x}=(\frac{2}{3})^{x}). Since (0<\frac{2}{3}<1), the function (y = a^{x}) with (0 < a<1) is an exponential - decay function.
Step2: Analyze key - points
When (x = 0), (f(0)=(\frac{2}{3})^{0}=1). As (x\to+\infty), (f(x)\to0) and as (x\to-\infty), (f(x)\to+\infty).
Answer:
The graph that starts at the point ((0,1)) and decreases as (x) increases (the second graph from the left in the given set of graphs).