Question

Which of the following statements is true?

Answer 1

I believe your answer is C.

Answer 2

Answer:

The correct option is C.

Step-by-step explanation:

The given function is

$f(x)=5^x-4$

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

$f(0)=5^(0)-4=1-4=-3$

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

$f(2)=5^2-4=25-4=21$

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

$m=\frac{f(2)-f(0)}{2-0}$

$m=\frac{21-(-3)}{2}=12$

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

$m=\frac{g(2)-g(0)}{2-0}$

$m=\frac{12-(-3)}{2}=7.5$

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.