Q. 45 - 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.

$f\left(x\right)=3·{\left(\frac{1}{2}\right)}^x$

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 $f\left(x\right)=3·{\left(\frac{1}{2}\right)}^x$

Step 2: Transforming and plotting the graph

The graph of $y={\left(\frac{1}{2}\right)}^x$ is 

Step 3: Streching the graph by a factor of 3

Multiply by a factor of three and plotting, we get

Step 4: Calculate domain, range and asymptote

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