1. **Stating the problem:** We are given points (0, -4), (1, -6), and (2, -9) and asked to identify the type of sequence or function they represent. 2. **Check if it is an arithmetic sequence:** An arithmetic sequence has a constant difference between consecutive terms. Calculate differences: $-6 - (-4) = -2$, $-9 - (-6) = -3$. Differences are not equal, so it is not arithmetic. 3. **Check if it is a geometric sequence:** A geometric sequence has a constant ratio between consecutive terms. Calculate ratios: $\frac{-6}{-4} = 1.5$, $\frac{-9}{-6} = 1.5$. Ratios are equal, but since terms are negative and decreasing, this suggests a geometric pattern with ratio 1.5. 4. **Check if it is a linear function:** A linear function has the form $y = mx + b$ with constant slope $m$. Calculate slope between points: Between (0, -4) and (1, -6): $m = \frac{-6 - (-4)}{1 - 0} = \frac{-2}{1} = -2$ Between (1, -6) and (2, -9): $m = \frac{-9 - (-6)}{2 - 1} = \frac{-3}{1} = -3$ Slopes are not equal, so it is not linear. 5. **Check if it is an exponential function:** An exponential function has the form $y = ab^x$. Using points (0, -4) and (1, -6): At $x=0$, $y = ab^0 = a = -4$ At $x=1$, $y = ab = -6$ so $b = \frac{-6}{-4} = 1.5$ Check at $x=2$: $y = a b^2 = -4 \times (1.5)^2 = -4 \times 2.25 = -9$, which matches the point (2, -9). 6. **Conclusion:** The points fit the exponential function $y = -4 \times 1.5^x$. **Final answer:** The data represents an exponential function.