Question

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

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

Short answer

The graph is

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

Step-by-step solution

Given information

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

Transform and graph

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

Shifting two units vertically upwards

The graph is

Calculate the domain and range

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