1. The problem asks which relationship represents a function with a lesser rate of change than the graphed function. 2. The graphed function passes through points approximately $(-2,5)$ and $(4,-5)$. 3. Calculate the slope (rate of change) of the graphed function using the formula: $$\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}$$ 4. Substitute the points: $$\text{slope} = \frac{-5 - 5}{4 - (-2)} = \frac{-10}{6} = -\frac{5}{3} \approx -1.67$$ 5. Calculate the slope for Table A: Points: $(-2,0)$ and $(4,-9)$ $$\text{slope}_A = \frac{-9 - 0}{4 - (-2)} = \frac{-9}{6} = -\frac{3}{2} = -1.5$$ 6. Calculate the slope for Table B: Points: $(-5,7)$ and $(1,-5)$ $$\text{slope}_B = \frac{-5 - 7}{1 - (-5)} = \frac{-12}{6} = -2$$ 7. Compare the slopes: - Graphed function slope: $-1.67$ - Table A slope: $-1.5$ - Table B slope: $-2$ 8. A lesser rate of change means a slope with smaller absolute value. 9. Since $|-1.5| < |-1.67|$ and $|-2| > |-1.67|$, Table A has a lesser rate of change than the graphed function. **Final answer:** Table A represents a function with a lesser rate of change than the graphed function.