Question

In Problems 41-52, use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function.

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

Short answer

The graph is

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

Step-by-step solution

Given information

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

Transform and graph

Substituting $x=x+3$, we get

$y=2^{x+3}$

The graph is

Reflecting about x axis and shifting one unit vertically downwards

The graph is

Calculate domain and range

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