draw the graph of f(x)=3^(-x). provide your answer below:
draw the graph of f(x)=3^(-x). provide your answer below:
Answer
Explanation:
Step1: Find the y - intercept
Set (x = 0). Then (f(0)=3^{-0}=1), so the graph passes through the point ((0,1)).
Step2: Find other points
When (x = 1), (f(1)=3^{-1}=\frac{1}{3}); when (x=- 1), (f(-1)=3^{-(-1)} = 3).
Step3: Analyze the behavior
As (x\rightarrow+\infty), (y = 3^{-x}=\left(\frac{1}{3}\right)^{x}\rightarrow0). As (x\rightarrow-\infty), (y = 3^{-x}\rightarrow+\infty). The function (y = 3^{-x}) is an exponential decay function.
Answer:
The graph is an exponential - decay curve passing through ((0,1)), decreasing as (x) increases, approaching the (x) - axis ((y = 0)) as (x\rightarrow+\infty) and going to (+\infty) as (x\rightarrow-\infty).