Q. 41 - 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.

$y=2^x+1$

Step-by-Step Solution

Answer

The graph is 

 and the domain, range is $(-\infty ,+\infty ),(1,+\infty )$ and the horizontal asymptote is $y=1$

Step 1: Given information

Given the function $f\left(x\right)=2^x+1$

Step 2:Transforming and plotting the graph

The graph of $y=2^x$ is 

Step 3: Shifting up by one unit

The graph is 

Step 4: Calculate domain, range and asymptote

On seeing the graph, the domain and range is $(-\infty ,+\infty )$ and $(1,+\infty )$ respectively and the horizontal asymptote is $y=1$