Chapter 4 - Exponential and Logarithmic Functions - Section 4.3 Exponential Functions - 4.3 Assess Your Understanding - Page 306: 42

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

Step 1. To obtain the graph of $f(x)=3^x-2$ from $y=3^x$, shift the curve 2 units down. See graph. Step 2. We can determine the domain $(-\infty,\infty)$, range $(-2,\infty)$, horizontal asymptote H.A. $y=-2$.