This question is solved using the concepts of average rate of change and y-intercept.
- First, the concepts are presented.
- Then, the average rate and the y-intercept are found for each of the functions.
- With the rates for each function, it is possible to find the correct option.
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:
[tex]A = \frac{f(b) - f(a)}{b - a}[/tex]
y-intercept:
The y-intercept of a function is the value of x when y = 0.
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Function f:
When [tex]x = 0[/tex], [tex]f(0) = 5^{0} - 4 = 1 - 4 = -3[/tex], that is, the y-intercept is -3.
When [tex]x = 2[/tex], [tex]f(2) = 5^2 - 4 = 25 - 4 = 21[/tex]
Thus, the average rate of change is:
[tex]A = \frac{21 - (-3)}{2 - 0} = \frac{24}{2} = 12[/tex]
Function g:
Looking at the graph, when [tex]x = 0, g(0) = -3[/tex], that is, the y-intercept is -3.
When [tex]x = 2, g(2) = 12[/tex].
Thus, the average rate of change is:
[tex]A = \frac{12 - (-3)}{2 - 0} = \frac{15}{2} = 7.5[/tex]
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Comparison:
- Average rate of change: For f is 12, for g is 7.5, so f is greater.
- y-intercept: For f it is -3, for g it is also -3, so same.
Thus, the correct answer is given by option A.
A similar question is found at https://brainly.com/question/20732437
