Problem
\[ f(x)=\left(\frac{2}{3}\right)^{-x} \] Plot five points on the graph of the function, and also draw the asymptote. Then click on the graph-a-function button.
Solution
Step 1 ：Given the function \(f(x)=(\frac{2}{3})^{-x}\).
Step 2 ：Choose five x-values such as -2, -1, 0, 1, 2 and calculate the corresponding y-values.
Step 3 ：The y-values are calculated as follows: \(f(-2) = 0.44444444\), \(f(-1) = 0.66666667\), \(f(0) = 1\), \(f(1) = 1.5\), and \(f(2) = 2.25\).
Step 4 ：Plot these five points on the graph of the function.
Step 5 ：As x approaches infinity, the function value approaches 0, so the asymptote of the function is y=0.
Step 6 ：\(\boxed{\text{The five points on the graph of the function are } (-2, 0.44444444), (-1, 0.66666667), (0, 1), (1, 1.5), \text{ and } (2, 2.25). \text{ The asymptote of the function is } y=0.}\)
