Fill in the blanks Suppose that the function f has the same average rate of change c between any two points. (a) Find the avera

Question

Fill in the blanks
Suppose that the function f has the same average rate of change c between any two points.
(a) Find the average rate of change of f between the points a and x to show that
c = f(x) − f(a)/ x-a

The rate of change between any two points is___________

Rearrange the equation in part (a) to show that
f(x) = cx + (f(a) − ca)

Multiplying the equation in part(a) by x − a, we obtain f(x) − f(a) = c(_________)

Rearranging and adding
f(a) to both sides, we have f(x) = cx + f(a) − (________), as desired.

How does this show that f is a linear function? What is the slope, and what is the y-intercept?

Because this equation is of form f(x) = Ax + B with constants A=_______ and
B = f(a) −____________ it represents a linear function with slope of _______ and y-intercept f(a) − ____________

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Ariana 1 week 2021-09-09T13:31:53+00:00 1 Answer 0

Answers ( )

    0
    2021-09-09T13:33:31+00:00

    Answer:

    Step-by-step explanation:

    Rate of change= slope/gradient (Constant of proportionality, slope, unit rate)

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