1. The problem is to graph the exponential function $f(x) = \left(\frac{3}{5}\right)^x$ and plot five points on its graph. 2. The general form of an exponential function is $f(x) = a^x$ where $a > 0$ and $a \neq 1$. Here, $a = \frac{3}{5}$ which is between 0 and 1, so the function is a decreasing exponential. 3. To plot points, substitute values of $x$ into the function and calculate $f(x)$: - For $x = -2$: $$f(-2) = \left(\frac{3}{5}\right)^{-2} = \left(\frac{5}{3}\right)^2 = \frac{25}{9} \approx 2.78$$ - For $x = -1$: $$f(-1) = \left(\frac{3}{5}\right)^{-1} = \frac{5}{3} \approx 1.67$$ - For $x = 0$: $$f(0) = \left(\frac{3}{5}\right)^0 = 1$$ - For $x = 1$: $$f(1) = \frac{3}{5} = 0.6$$ - For $x = 2$: $$f(2) = \left(\frac{3}{5}\right)^2 = \frac{9}{25} = 0.36$$ 4. These points are: $(-2, 2.78)$, $(-1, 1.67)$, $(0, 1)$, $(1, 0.6)$, and $(2, 0.36)$. 5. Plot these points on the coordinate grid and draw a smooth curve through them to graph the function. 6. The graph will show a decreasing curve approaching the x-axis but never touching it, since $f(x) > 0$ for all $x$. Final answer: The function $f(x) = \left(\frac{3}{5}\right)^x$ is a decreasing exponential with plotted points as above.