1. The problem is to identify which function corresponds to each graph based on their descriptions and the given functions. 2. The functions are: - $n(x) = 6.6(0.6)^x$ - $k(x) = 6.6(1.6)^x$ - $g(x) = 1.4(3)^x$ - $h(x) = 3.4(0.6)^x$ 3. Important rules for exponential functions: - If the base is between 0 and 1 (e.g., 0.6), the function is exponential decay. - If the base is greater than 1 (e.g., 1.6 or 3), the function is exponential growth. - The coefficient before the base affects the starting value (y-intercept at $x=0$). 4. Analyze each graph: - Top-left graph: exponential decay starting near 7 at $x=-5$, decreasing towards 0 as $x$ increases. - Top-right graph: exponential decay starting near 7 at $x=-5$, decreasing towards 0, but slightly different shape. - Bottom-left graph: exponential growth starting near 1 at $x=-5$, increasing steeply to 8 at $x=5$. - Bottom-right graph: exponential growth starting near 1 at $x=-5$, increasing very steeply to 8 at $x=5$. 5. Match functions to graphs: - For decay with starting value near 7, check $n(x)$ and $h(x)$ since they have base 0.6. - $n(0) = 6.6(0.6)^0 = 6.6$, $h(0) = 3.4(0.6)^0 = 3.4$ so top-left graph with starting near 7 matches $n(x)$. - Top-right graph with decay but different shape and lower starting value matches $h(x)$. - For growth starting near 1, check $g(x)$ and $k(x)$. - $g(0) = 1.4(3)^0 = 1.4$, $k(0) = 6.6(1.6)^0 = 6.6$. - Bottom-left graph starting near 1 matches $g(x)$. - Bottom-right graph with very steep growth and higher starting value matches $k(x)$. Final matching: - Top-left: $n(x) = 6.6(0.6)^x$ - Top-right: $h(x) = 3.4(0.6)^x$ - Bottom-left: $g(x) = 1.4(3)^x$ - Bottom-right: $k(x) = 6.6(1.6)^x$