Q. 48 - 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

$f\left(x\right)=-3^x+1$

Step-by-Step Solution

Answer

The graph is 

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

Step 1: Given information

Given function $f\left(x\right)=-3^x+1$

Step 2: Transforming and plotting the graph

The graph of $y=3^{-x}$ is 

Step 3: Shifting graph one unit vertically upwards

The graph is

Step 4: Calculate the domain and range

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