Q. 42 - 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 $3^x$ is 

Step 3: Shifting down by one unit

The graph of $y=3^x-2$ is 

Step 4: Calculate domain, range and asymptote

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