Q. 49 - 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.

$f\left(x\right)=2+4^{x-1}$

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 $f\left(x\right)=2+4^{x-1}$

Step 2: Transform and plot the graph

Substituting $x=x-1$ and plotting , we get

Step 3: Shift two units vertically upwards

The graph is 

Step 4: Calculate the domain and range

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