1. **Problem Statement:** Match each exponential function formula to its corresponding graph based on the description of the curve and key points. 2. **Recall the general form:** An exponential function is generally $f(x) = a^x$ where $a > 0$. - If $a > 1$, the function is increasing. - If $0 < a < 1$, the function is decreasing. - A negative sign in front of the function reflects it across the x-axis. - All exponential functions pass through the point $(0,1)$ if positive, or $(0,-1)$ if multiplied by -1. 3. **Analyze each formula:** - a. $f(x) = 4^x$: Since $4 > 1$, this is an increasing exponential passing through $(0,1)$. - b. $f(x) = \left(\frac{1}{4}\right)^x$: Since $\frac{1}{4} < 1$, this is a decreasing exponential passing through $(0,1)$. - c. $f(x) = -4^x$: This is the negative of an increasing exponential, so it is decreasing and passes through $(0,-1)$. - d. $f(x) = -\left(\frac{1}{4}\right)^x$: This is the negative of a decreasing exponential, so it is increasing and passes through $(0,-1)$. 4. **Match to graphs:** - Graph 1 (top-left): Increasing exponential through $(0,1)$ rising steeply. Matches a. $4^x$. - Graph 2 (top-right): Decreasing exponential through $(0,-1)$ descending steeply. Matches c. $-4^x$. - Graph 3 (bottom-left): Decreasing exponential through $(0,1)$ approaching zero as $x$ increases. Matches b. $\left(\frac{1}{4}\right)^x$. - Graph 4 (bottom-right): Increasing exponential through $(0,-1)$ rising towards zero from below as $x$ goes left. Matches d. $-\left(\frac{1}{4}\right)^x$. **Final matches:** - a. $4^x$ → Graph 1 - b. $\left(\frac{1}{4}\right)^x$ → Graph 3 - c. $-4^x$ → Graph 2 - d. $-\left(\frac{1}{4}\right)^x$ → Graph 4