1. The problem asks to construct tables of ordered pairs for four exponential functions and sketch their graphs. 2. For each function, calculate $y$ at several values of $x$ (e.g., $-2$, $-1$, $0$, $1$, $2$). \textbf{Function 61: } $y = 4^x$ - $x = -2$, $y = 4^{-2} = \frac{1}{4^2} = \frac{1}{16} = 0.0625$ - $x = -1$, $y = 4^{-1} = \frac{1}{4} = 0.25$ - $x = 0$, $y = 4^0 = 1$ - $x = 1$, $y = 4^1 = 4$ - $x = 2$, $y = 4^2 = 16$ \textbf{Function 62: } $y = 5^x$ - $x = -2$, $y = 5^{-2} = \frac{1}{5^2} = \frac{1}{25} = 0.04$ - $x = -1$, $y = 5^{-1} = \frac{1}{5} = 0.2$ - $x = 0$, $y = 5^0 = 1$ - $x = 1$, $y = 5^1 = 5$ - $x = 2$, $y = 5^2 = 25$ \textbf{Function 63: } $y = \left(\frac{1}{4}\right)^x$ - Note $\left(\frac{1}{4}\right)^x = 4^{-x}$, so values are reversed from function 61. - $x = -2$, $y = 4^{2} = 16$ - $x = -1$, $y = 4^{1} = 4$ - $x = 0$, $y = 1$ - $x = 1$, $y = \frac{1}{4} = 0.25$ - $x = 2$, $y = \frac{1}{16} = 0.0625$ \textbf{Function 64: } $y = \left(\frac{1}{5}\right)^x$ - Note $\left(\frac{1}{5}\right)^x = 5^{-x}$, similarly reversed from function 62. - $x = -2$, $y = 5^{2} = 25$ - $x = -1$, $y = 5^{1} = 5$ - $x = 0$, $y = 1$ - $x = 1$, $y = \frac{1}{5} = 0.2$ - $x = 2$, $y = \frac{1}{25} = 0.04$ 3. The graphs have these shapes: - $y = 4^x$ and $y=5^x$ are exponential growth curves, starting near zero at negative $x$ and increasing steeply. - $y = (1/4)^x$ and $y = (1/5)^x$ are exponential decay curves, starting large at negative $x$ and approaching zero as $x$ increases. These tables allow sketching the graphs accurately.