If f is an increasing function what can you say about f2 com

If f is an increasing function, what can you say about f(2) compared to f(5)? What is the average rate of change of G(x) = 2x - 5 between the points (3, 1)and (5, 5)? The function G(x) is either increasing or decreasing everywhere. Explain how your answer to part (a) tells you which.

Solution

1)

Since f(x) is incraesing function, as x will increase, f(x) will also increase.

Therfore, f(5) is larger than f(2)

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2)

a)

Average rate of change =(5-1)/(5-3) = 4/2 =2

Therfore, Average rate of change of change is 2.

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b)

Here average rate of change is same as the slope of the line and this slope is constant for any two points chosen.

Since slope is postive, the G(x) is increasing function.