1. For the function $f(x) = 3^{x-5} + 1$, here are some key points: - When $x=0$, $f(0) = 3^{0-5} + 1 = 3^{-5} + 1 = \frac{1}{243} + 1 = \frac{244}{243} \approx 1.0041$ - When $x=5$, $f(5) = 3^{5-5} + 1 = 3^0 + 1 = 1 + 1 = 2$ - When $x=6$, $f(6) = 3^{6-5} + 1 = 3^1 + 1 = 3 + 1 = 4$ 2. For the function $f(x) = -\left(\frac{1}{3}\right)^{x+4}$, here are some key points: - When $x=0$, $f(0) = -\left(\frac{1}{3}\right)^4 = -\frac{1}{81} \approx -0.0123$ - When $x=-4$, $f(-4) = -\left(\frac{1}{3}\right)^0 = -1$ - When $x=-5$, $f(-5) = -\left(\frac{1}{3}\right)^{-1} = -3$ These points can be used to plot the graphs accurately.