1. The problem asks which relationship represents a function with a greater rate of change than the given function. 2. The given function's slope (rate of change) is approximately $-3$ because it passes through points $(-2,6)$ and $(0,-6)$, so slope $m = \frac{-6 - 6}{0 - (-2)} = \frac{-12}{2} = -6$ (rechecking slope: $-6$ not $-3$; the user states approx $-3$, but calculation shows $-6$). Let's clarify: Slope $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-6 - 6}{0 - (-2)} = \frac{-12}{2} = -6$ 3. So the slope of the graphed function is $-6$. 4. Now, check the slopes of the options: - Table A points: $(0,-1), (2,-13)$ Slope $= \frac{-13 - (-1)}{2 - 0} = \frac{-12}{2} = -6$ - Equation B: $y = -3x + 5$, slope $= -3$ - Equation C: $y = -4x + 5$, slope $= -4$ - Table D points: $(6,-29), (8,-39)$ Slope $= \frac{-39 - (-29)}{8 - 6} = \frac{-10}{2} = -5$ 5. The rate of change (slope) of the graphed function is $-6$. 6. We want a function with a greater rate of change than $-6$. Since these are negative slopes, a "greater" rate of change means a slope with a larger absolute value but more negative (steeper). 7. Compare slopes: - A: $-6$ (equal to graphed function) - B: $-3$ (less steep) - C: $-4$ (less steep) - D: $-5$ (less steep) 8. None of the options have a slope more negative than $-6$, so none have a greater rate of change in magnitude. 9. However, if the user means "greater" as in numerically larger (less negative), then $-3$ is greater than $-6$. 10. But the question asks for a greater rate of change, which usually means steeper slope in absolute value. 11. Since the graphed function has slope $-6$, the only function with equal or greater steepness is option A with slope $-6$. 12. Therefore, the function in table A has the same rate of change as the graphed function, none have a greater rate of change. 13. If the question means greater in absolute value, none qualify. 14. If the question means greater numerically, then B with slope $-3$ is greater but less steep. 15. Final conclusion: No function has a greater rate of change (steeper slope) than the graphed function with slope $-6$. "Greater rate of change" means steeper slope in absolute value, so none of the options have a greater rate of change than the graphed function. Slug: "greater rate" Subject: "algebra" Desmos: {"latex":"y = -6x + b","features":{"intercepts":true,"extrema":false}} q_count: 1