Question

Find the average rate of change for the function between the given values. f(x)=3x−2; from 4 to 7.

a) 2
b) 7
c) 3
d) 10

Answer 1

(c)

Step-by-step explanation:

the average rate of change of f(x) in the closed interval [ a, b ] is

`(f(b)-f(a))/(b-a)`

here [ a, b ] = [ 4, 7 ] , then

f(b) = f(7) = 3(7) - 2 = 21 - 2 = 19

f(a) = f(4) = 3(4) - 2 = 12 - 2 = 10

Then

average rate of change =
`(19-10)/(7-4)` =
`(9)/(3)` = 3

Answer 2

To find the average rate of change for the function f(x) = 3x - 2, we need to calculate the slope of the line connecting the given points. The slope can be calculated using the formula: (change in y) / (change in x). Using this formula, the average rate of change for the function from 4 to 7 is 3.

Step-by-step explanation:

To find the average rate of change for the function, we need to calculate the slope of the line connecting the two given points. The formula for finding the slope of a line passing through two points is:

Slope = (change in y)/(change in x)

Using the given points, we have:
Point 1: (4, f(4)) = (4, 3(4) - 2) = (4, 10)
Point 2: (7, f(7)) = (7, 3(7) - 2) = (7, 19)

Using the slope formula, we can calculate the average rate of change:
Slope = (19 - 10) / (7 - 4) = 9 / 3 = 3