The functions f and g are shown below. which of the following statements is true.

A: Over the intervals (0,2), The average rate of change of F is greater than that of G. The Y intercept of earth is the same as the Y intercept of G

B: over the intervals (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.

C: Over the intervals of (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.

D: Over the intervals (0,2) The average rate of change of F is the same as that of G. The Y intercept is greater than the Y intercept of G.

This question is solved using the concepts of average rate of change and y-intercept.

Doing this, the correct option is:

A: Over the intervals (0,2), The average rate of change of F is greater than that of G. The Y intercept of earth is the same as the Y intercept of G

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Average rate of change:

The average rate of change of a function f(x) in an interval [a,b] is given by:

y-intercept:

The y-intercept of a function is the value of x when y = 0.

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Function f:

When , , that is, the y-intercept is -3.

When ,

Thus, the average rate of change is:

Function g:

Looking at the graph, when , that is, the y-intercept is -3.

When .

Thus, the average rate of change is:

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Comparison:

Thus, the correct answer is given by option A.

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