1. **Problem:** Match each function with its corresponding graph. 2. **Recall the properties of exponential functions:** - $f(x) = a^x$ is an increasing function if $a > 1$. - $f(x) = a^{-x} = \frac{1}{a^x}$ is a decreasing function. - Vertical shifts add or subtract a constant to the function. - Reflections multiply the function by $-1$. 3. **Analyze each function:** - $f(x) = 5^{-x}$ is a decreasing exponential, crossing $y=1$ at $x=0$. - $f(x) = 5^x$ is an increasing exponential, crossing $y=1$ at $x=0$. - $f(x) = 5^{x+1} - 4 = 5 \cdot 5^x - 4$ shifts the graph of $5^x$ left by 1 and down by 4. - $f(x) = 5^x + 3$ shifts the graph of $5^x$ up by 3. - $f(x) = -5^x$ reflects $5^x$ across the x-axis. 4. **Match with graphs:** - Graph B: Decreasing exponential crossing $y=1$ at $x=0$ matches $f(x) = 5^{-x}$. - Graph C: Increasing exponential crossing $y=1$ at $x=0$ matches $f(x) = 5^x$. - Graph D: Shifted left and down, matches $f(x) = 5^{x+1} - 4$. - Graph E: Shifted up, matches $f(x) = 5^x + 3$. - Graph A: Negative reflection of $5^x$, matches $f(x) = -5^x$. **Final matching:** 1. $f(x) = 5^{-x}$ → Graph B 2. $f(x) = 5^x$ → Graph C 3. $f(x) = 5^{x+1} - 4$ → Graph D 4. $f(x) = 5^x + 3$ → Graph E 5. $f(x) = -5^x$ → Graph A