Chapter 5 - Exponential and Logarithmic Functions - 5.3 Exponential Functions - 5.3 Assess Your Understanding - Page 281: 49

See below.

Step 1. To obtain the graph of $f(x)=3^{-x}-2$ from $y=3^{x}$, reflect the curve across the y-axis, then shift 2 units down. See graph. Step 2. We can determine the domain is $(-\infty,\infty)$; the range is $(-2,\infty)$; and the horizontal asymptote is $y=-2$.