Which of the following statements is true?
a.
over the interval [0, 2], the average rate of change of f is the same as that of g. the y-intercept of f is less than the y-intercept of g.
b.
over the interval [0, 2], the average rate of change of f is the same as that of g. the y-intercept of f is greater than the y-intercept of g.
c.
over the interval [0, 2], the average rate of change of f is greater than that of g. the y-intercept of f is the same as the y-intercept of g.
d.
over the interval [0, 2], the average rate of change of f is less than that of g. the y-intercept of f is the same as the y-intercept of g.

The correct option is C.

Step-by-step explanation:

The given function is

Put x=0, to find the y-intercept.

The y-intercept of f(x) is -3.

From the given graph it is clear that the graph of g(x) intersect the y-axis at -3, so the y-intercept of g(x) is -3.

Therefore the y-intercepts of both the functions f(x) and g(x) are same.

At x=2, then value of function is

The average rate of change of f over the interval [0,2] is

The average rate of change of f  over the interval [0,2] is 12.

From the given graph it is clear that the graph of g(x) is passing through the points (0,-3) and (2,12).

The average rate of change of g over the interval [0,2] is

The average rate of change of g over the interval [0,2] is 7.5.

The over the interval [0, 2], the average rate of change of f is greater than that of g. Therefore the correct option is C.

2/3

step-by-step explanation: