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3 years ago

Consider the table of values for functions f and g below.

Mathematics

1 answer:

AlexFokin [52]3 years ago

6 0

Answer:

A. For every value of x, the rate of change of f exceeds the rate of change of g.

FALSE

Because the rate of change of f increases from 4 to 294, while the rate of change of g is constant (8).

B. As x increases, the rate of change of g exceeds the rate of change of f.

FALSE.

Because the rate of change of g is 8 (constant) and the rate of change of f starts at 4 and increases exceeding that of g.

C. At x = 2, the rate of change of f is equal to the rate of change of g.

FALSE

At x = 2 the rate of change of f is 12 and the rate of change of g is 8.

D. As x increases, the rate of change of f exceeds the rate of change of g.

TRUE

The rate of change of f at start is 4 and increases to 294, while the rate of change of g is 8 (constant), so as x increases, the rate of change of f exceeds the rate of change of g.

Explanation:

The rate of change of a function is calculated as:

rate of change = rise / run = change in y / change in x = Δy / Δx

For f(x) you get the following rates of change:

x f(x) Δy Δx Δy/Δx

0 3 - - -

1 7 7-3 = 4 1 - 0 = 1 4/1 = 4

2 19 19 - 7 = 12 2 - 1 = 1 12/1 = 12

3 55 55 - 19 = 36 3 - 2 = 1 36

4 163 163 - 55 = 108 4 - 3 = 2 108

5 457 457 - 163 = 294 5 - 4 = 1 294

From that, you see that the function f(x) is an increasing function with an increasing rate of change in the interval [0,5].

For g(x) you get f(x) you get the following rates of change:

x g(x) Δy Δx Δy/Δx

0 3

1 11 11 - 3 = 8 1 - 0 = 1 8

2 19 19 - 11 = 8 2 - 1 = 1 8

3 27 27 - 19 = 8 3 - 2 = 1 8

4 35 35 - 27 = 8 4 - 3 = 1 8

5 43 43 - 35 = 8 5 - 4 = 1 8

From that you can see that the function f(x) is increasing linear function, so its rates of change is constant.

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irakobra [83]

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