Answer:
The correct option is C.
Step-by-step explanation:
The given function is
[tex]f(x)=5^x-4[/tex]
Put x=0, to find the y-intercept.
[tex]f(0)=5^(0)-4=1-4=-3[/tex]
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
[tex]f(2)=5^2-4=25-4=21[/tex]
The average rate of change of f over the interval [0,2] is
[tex]m=\frac{f(2)-f(0)}{2-0}[/tex]
[tex]m=\frac{21-(-3)}{2}=12[/tex]
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
[tex]m=\frac{g(2)-g(0)}{2-0}[/tex]
[tex]m=\frac{12-(-3)}{2}=7.5[/tex]
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.
