What is the average rate of change of f(x)=(1)/(2)x-7 from x=2 to x=10 ?

Question

What is the average rate of change of
`f(x)=(1)/(2)x-7` from
`x=2` to
`x=10` ?

Answer 1

1/2

Explanation:

You want to know the average rate of change of f(x) = 1/2x -7 on the interval [2, 10].

Linear function

A linear function has the same rate of change everywhere. Its instantaneous rate of change, average rate of change, and slope are all the same constant.

The given function is written in slope-intercept form, so we can identify the slope as the coefficient of x: 1/2.

The average rate of change is 1/2.

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Additional comment

If you feel the need to "show work", you can evaluate ...

AROC = (f(10) -f(2))/(10 -2) = (-2 -(-6))/8 = 4/8 = 1/2