Question

two functions are shown. function a (table with x and y values) and function b (graph). question: what function with the greater rate of change? options: function a, function b

Explanation:

Step1: Find rate of change for Function A

The rate of change (slope) for a function from a table is calculated as $\frac{\Delta y}{\Delta x}$. Using two points from Function A's table, say $(x_1,y_1)=(-2, -1)$ and $(x_2,y_2)=(-1, 2)$. Then $\Delta y = 2 - (-1)=3$, $\Delta x=-1 - (-2)=1$. So rate of change for A is $\frac{3}{1}=3$.

Step2: Find rate of change for Function B

For a linear graph (Function B), pick two points on the line. From the graph, let's take $(0, 1)$ and $(1, 3)$. Then $\Delta y = 3 - 1 = 2$, $\Delta x=1 - 0 = 1$. So rate of change for B is $\frac{2}{1}=2$.

Step3: Compare the rates

Since $3>2$, Function A has a greater rate of change.

Answer:

Function A