Q. 47 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 41-52, use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function.

$f\left(x\right)=3^{-x}-2$

Step-by-Step Solution

Answer

The graph is 

 and the domain and range is $(-\infty ,+\infty ),(-2,+\infty )$ and the horizontal asymptote is $y=-2$

Step 1: Given information

Given function $f\left(x\right)=3^{-x}-2$

Step 2: Transforming and plotting the graph

The graph of $y=3^{-x}$ is 

Step 3: Shifting two units vertically downwards

The graph is 

Step 4: Calculating the domain and range

The domain and range is $(-\infty ,+\infty ),(-2,+\infty )$ and the horizontal asymptote is $y=-2$