Question

A table of values for function f(x) is shown below. Find the average rate of change between each of the following sets of x-values. Show all work that leads to your answer.X has 0, 2, 4, 6, 8, 10, and Y has 0, -4, 0, 12, 32, and 60(a) x=0 to x=6(b) 4 less than or equal to X less than or equal to 10

Answer 1

a) 2

b) 10

Step-by-step explanation:

The values of x and y given:

X has 0, 2, 4, 6, 8, 10

Y has 0, -4, 0, 12, 32, and 60

We are to find the average rate of change using the formula:

`\text{Average rate of change = }\frac{f(b)\text{ - f(a)}}{b\text{ - a}}`

a) from x = 0 to x = 6

let b = 6, a = 0

We need to check the corresponding y values for x = 0 and x = 6

when x = 0, y = 0; f(a) = 0

when x = 6, y = 12; f(b) = 12

`\begin{gathered} \text{Average rate of change =}\frac{12\text{ - 0}}{6-0} \\ \text{Average rate of change = }(12)/(6)\text{ = 2} \end{gathered}`

b) 4 less than or equal to X less than or equal to 10

This is written as:

4 ≤ x ≤10

a = 4, b = 10

We need to check the corresponding y values for x = 4, and x = 10

when x = 4, y = 0; f(a) = 0

when x = 10, y = 60; f(b) = 60

`\begin{gathered} \text{Average rate of change = }\frac{60\text{ - 0}}{10\text{ - 4}} \\ \text{Average rate of change = }(60)/(6) \\ \text{Average rate of change = 10} \end{gathered}`