the rate of change are equal (option A)
Explanation:
To find which of the function has a greater rate of change, we need to find the slope of the graph as well as the slope of the table. Then we will compare the result.
The slope formula:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]
The points on the graph to be used: (0, 1) , (1, 2)
[tex]\begin{gathered} x_1=0,y_1=1,x_2=1,y_2\text{ = }2 \\ \text{slope = m = }\frac{2\text{ - 1}}{1-\text{ 0}} \\ \text{slope = 1/1} \\ \text{slope = 1} \end{gathered}[/tex]
We will pick any two points on the table:
Using points (1, 2) and (2, 3)
[tex]\begin{gathered} x_1=1,y_1=2,x_2=2,y_2\text{ = }3 \\ \text{slope = }\frac{3\text{ - 2}}{2\text{ - 1}} \\ \text{slope = 1/1} \\ \text{slope = 1} \end{gathered}[/tex]
From our calculations, we see the slope of the graph and the slope of the table are the same.
Hence, the rate of change are equal (option A)
