Q. 51 - 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.

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

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 $f\left(x\right)=2+3^{x/2}$

Step 2: Transform and graph

Substituting $x=\frac{x}{2}$, the graph is 

Step 3: Shifting two units vertically upwards

The graph is 

Step 4: Calculate the domain and range

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