Question

20 points please!!! helpp with functions and average rate of change

Answer 1

option C.

Explanation:

If we calculate average rate of change of a function over a certain interval, we’re computing the average number of units which the function moves up or down, per unit along on the xx-axis. We might alternatively argue that we’re measuring how much change occurs in our function’s value per unit on the xx-axis.

The equation for average rate of change is -

Δx/Δf =

f(x2) - f(x1) / x2 - x1

Answer 2

C k(x)

Explanation:

The average rate of change (m) of a function on an interval is the difference between the function values at the ends of the interval, divided by the interval width:

`m_(ab)=(f(b)-f(a))/(b-a)\qquad\text{average rate of change on interval $[a,b]$}`

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simplification

Here, the interval of concern is the same for all of the functions. It is [a, b] = [0, 2] so the denominator of this fraction is 2-0 = 2 for all of the functions. That means we can determine the greatest average rate of change by simply looking at the differences f(2) -f(0) for each of the functions.

amount of change

A. j(2) -j(0) = 3(1.6²) -3 = 4.68

B. g(2) -g(0) = 25/2 -8 = 9/2 = 4.5

C. k(2) -k(0) = 9 -4 = 5 . . . . . . . . . . greatest amount of change

D. f(2) -f(0) = 1.5(2²) -1.5 = 4.5

solution

The function k(x) has the greatest average rate of change over the interval [0, 2].