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

x f(x) g(x)
0 3 3
1 7 11
2 19 19
3 55 27
4 163 35
5 457 43

which of the following statements is true?

a.
for every value of x, the rate of change of f exceeds the rate of change of g.
b.
as x increases, the rate of change of g exceeds the rate of change of f.
c.
at x = 2, the rate of change of f is equal to the rate of change of g.
d.
as x increases, the rate of change of f exceeds the rate of change of g.

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:

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.

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is symmetric about the line y = 120,000.

step-by-step explanation:

the photograph is photographer and- in the process- ourselves.

step-by-step explanation: