Chapter 4 - Exponential and Logarithmic Functions - Section 4.3 Exponential Functions - 4.3 Assess Your Understanding - Page 306: 51

See graph. domain $(-\infty,\infty)$, range $(2,\infty)$, H.A. $y=2$.

Step 1. To obtain the graph of $f(x)=2+3^{x/2}$ from $y=3^x$, stretch the curve horizontally by a factor of 2, then shift 2 units up. See graph. Step 2. We can determine the domain $(-\infty,\infty)$, range $(2,\infty)$, horizontal asymptote H.A. $y=2$.