1. **State the problem:** We need to match each exponential function to its corresponding graph based on their behavior and points. 2. **Recall the properties of exponential functions:** - For $f(x) = a^x$ with $a > 1$, the function is increasing. - For $f(x) = a^x$ with $0 < a < 1$, the function is decreasing. - All exponential functions pass through the point $(0,1)$ because $a^0 = 1$. 3. **Analyze each function:** - $v(x) = 3^x$: base $3 > 1$, so increasing rapidly. - $s(x) = 2^x$: base $2 > 1$, increasing but slower than $3^x$. - $w(x) = \left(\frac{3}{2}\right)^x$: base $1.5 > 1$, increasing slower than $2^x$. - $t(x) = \left(\frac{1}{2}\right)^x$: base $0.5 < 1$, so decreasing. 4. **Analyze the graphs:** - Graph 1: decreasing exponential curve passing through $(0,1)$, $(−1,2)$, $(−2,4)$, approaching 0 as $x$ increases. - Graph 2: increasing exponential curve passing through $(0,1)$, rising slowly to the right, about $(1,1.5)$. 5. **Match the functions to graphs:** - Graph 1 is decreasing, so it matches $t(x) = \left(\frac{1}{2}\right)^x$. - Graph 2 is increasing slowly, so it matches $w(x) = \left(\frac{3}{2}\right)^x$. 6. **Summary:** - $t(x) = \left(\frac{1}{2}\right)^x$ matches Graph 1. - $w(x) = \left(\frac{3}{2}\right)^x$ matches Graph 2. Note: The problem only provides two graphs, so $v(x)$ and $s(x)$ are not matched here. **Final answer:** - Graph 1: $t(x) = \left(\frac{1}{2}\right)^x$ - Graph 2: $w(x) = \left(\frac{3}{2}\right)^x$