Q. 44 - 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.

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

Step-by-Step Solution

Answer

The graph is 

 and the domain and range is $(-\infty ,+\infty ),(0,+\infty )$ and the horizontal asymptote is $y=0$

Step 1: Given information

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

Step 2: Transforming and plotting the graph

The graph of $2^x$ is 

Step 3: Move the graph by two units and plot

The graph of $f\left(x\right)=2^{x+2}$ is 

Step 4: Calculate domain, range and asymptote

From the graph, the domain and range is $(-\infty ,+\infty ),(0,+\infty )$ and the horizontal asymptote is $y=0$