Question

Which of the following statements is true?

Answer 1

Answer:

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.

Step-by-step explanation:

The function i.e mentioned in the question is

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

Now Placing x = 0, to compute the y-intercept

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

f(x) y-intercept is -3

As we can see in the given graph the graph of g(x) intersects the y-axis at -3

Therefore the y-intercept of g(x) is -3.

Hence, both functions with respect to the y-intercepts i.e f(x) and g(x) would remain the same

Now At x=2,

So, the value of the function is

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

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

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

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

From the mentioned graph as we can see that the graph of g(x) is crossing through the points (0,-3) and (2,12).

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

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

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

Therefore this is the correct answer but the same is not provided in the given options