Q. 50 - 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.

$f\left(x\right)=1-2^{x+3}$

Step-by-Step Solution

Answer

The graph is 

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

Step 1: Given information

Given function $f\left(x\right)=1-2^{x+3}$

Step 2: Transform and graph

Substituting $x=x+3$, we get

$y=2^{x+3}$

The graph is 

Step 3: Reflecting about x axis and shifting one unit vertically downwards

The graph is 

Step 4: Calculate domain and range

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