1. The problem is to match each given function with its corresponding graph based on the description of the curves. 2. The functions are: - $w(x) = -4(3)^{x+2}$ - $g(x) = 4\left(\frac{1}{3}\right)^{x+2}$ - $c(x) = -4(3)^{x-5}$ - $p(x) = 4\left(\frac{1}{3}\right)^{x-5}$ 3. Important rules: - For $a^x$ with $a>1$, the function grows exponentially as $x$ increases. - For $\left(\frac{1}{a}\right)^x$ with $a>1$, the function decreases exponentially as $x$ increases. - Negative coefficients reflect the graph across the x-axis. - Horizontal shifts inside the exponent affect where the graph is shifted left or right. 4. Analyze each function: - $w(x) = -4(3)^{x+2}$: Base 3 (growth), negative coefficient flips it down, shifted left by 2. - $g(x) = 4\left(\frac{1}{3}\right)^{x+2}$: Base $\frac{1}{3}$ (decay), positive coefficient, shifted left by 2. - $c(x) = -4(3)^{x-5}$: Base 3 (growth), negative coefficient flips it down, shifted right by 5. - $p(x) = 4\left(\frac{1}{3}\right)^{x-5}$: Base $\frac{1}{3}$ (decay), positive coefficient, shifted right by 5. 5. Match with graphs: - Graph 1: Decreasing steeply from left to minimum near $y=-10$ at $x=-2$, flattening near 0 on right. This matches $w(x)$ because of negative coefficient and shift left by 2. - Graph 2: Starts very high near $y=10$ at $x=-8$, decreases steeply approaching 0 as $x$ increases. Matches $g(x)$ with positive coefficient, decay base, shifted left by 2. - Graph 3: Starts very high near $y=10$ at $x=-8$, decreases steeply approaching 0 as $x$ increases, but negative coefficient flips it down. Matches $c(x)$ shifted right by 5. - Graph 4: Decreasing steeply from near 0 on left, passing around (3,0), then sharply down to about $y=-10$ near $x=10$. Matches $p(x)$ shifted right by 5. Final matches: - Graph 1: $w(x) = -4(3)^{x+2}$ - Graph 2: $g(x) = 4\left(\frac{1}{3}\right)^{x+2}$ - Graph 3: $c(x) = -4(3)^{x-5}$ - Graph 4: $p(x) = 4\left(\frac{1}{3}\right)^{x-5}$