1. **State the problem:** We need to graph the exponential function $$f(x) = \left(\frac{1}{2}\right)^{-x}$$ and plot five points on its graph, as well as draw the asymptote. 2. **Rewrite the function:** Recall that $$\left(\frac{1}{2}\right)^{-x} = 2^x$$ because $$a^{-b} = \frac{1}{a^b}$$ and here $$a=\frac{1}{2}$$ so $$\left(\frac{1}{2}\right)^{-x} = 2^x$$. 3. **Identify the asymptote:** For exponential functions of the form $$y = a^x$$ where $$a > 0$$ and $$a \neq 1$$, the horizontal asymptote is $$y=0$$. 4. **Calculate five points:** Choose five values of $$x$$ and compute $$f(x) = 2^x$$: - For $$x = -2$$: $$f(-2) = 2^{-2} = \frac{1}{2^2} = \frac{1}{4} = 0.25$$ - For $$x = -1$$: $$f(-1) = 2^{-1} = \frac{1}{2} = 0.5$$ - For $$x = 0$$: $$f(0) = 2^0 = 1$$ - For $$x = 1$$: $$f(1) = 2^1 = 2$$ - For $$x = 2$$: $$f(2) = 2^2 = 4$$ 5. **Summary:** The five points to plot are $$(-2, 0.25), (-1, 0.5), (0, 1), (1, 2), (2, 4)$$ and the horizontal asymptote is the line $$y=0$$. This completes the graphing of the function $$f(x) = \left(\frac{1}{2}\right)^{-x}$$.