45 this question is worth 2 credits. function a and function b are shown below. function a function b x y -5…

45 this question is worth 2 credits. function a and function b are shown below. function a function b x y -5 -30 -3 -18 2 12 4 24 which function has a greater rate of change? be sure to include the rate of change for each function in your answer. explain how you determined your answer.

45 this question is worth 2 credits. function a and function b are shown below. function a function b x y -5 -30 -3 -18 2 12 4 24 which function has a greater rate of change? be sure to include the rate of change for each function in your answer. explain how you determined your answer.

Answer

Explanation:

Step1: Find rate of change for Function A

The rate of change (slope) for a linear function is calculated as $\frac{y_2 - y_1}{x_2 - x_1}$. Using two points from Function A's table, e.g., $(-5, -30)$ and $(-3, -18)$: $\frac{-18 - (-30)}{-3 - (-5)} = \frac{12}{2} = 6$. We can verify with another pair, like $(2, 12)$ and $(4, 24)$: $\frac{24 - 12}{4 - 2} = \frac{12}{2} = 6$. So rate of change for A is 6.

Step2: Find rate of change for Function B

Function B is a line. Using two points from its graph, e.g., $(0, 0)$ and $(6, 3)$: $\frac{3 - 0}{6 - 0} = \frac{3}{6} = 0.5$. So rate of change for B is 0.5.

Step3: Compare the rates

Since $6 > 0.5$, Function A has a greater rate of change.

Answer:

Function A has a greater rate of change. The rate of change for Function A is 6 (calculated using the slope formula $\frac{y_2 - y_1}{x_2 - x_1}$ with points from its table, e.g., $\frac{-18 - (-30)}{-3 - (-5)} = 6$). The rate of change for Function B is 0.5 (calculated using points from its graph, e.g., $\frac{3 - 0}{6 - 0} = 0.5$). Since $6 > 0.5$, Function A's rate of change is greater.