Question

Determine which function has the greater rate of change in problems 1-3A. The rates of change are equal B. The graph has a greater rate of changeC. The table has a greater rate of change D. None of the above

Answer 1

the rate of change are equal (option A)

Step-by-step 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:

`m\text{ = }(y_2-y_1)/(x_2-x_1)`

The points on the graph to be used: (0, 1) , (1, 2)

`\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}`

We will pick any two points on the table:

Using points (1, 2) and (2, 3)

`\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}`

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)