Question

select the correct answer.
the table represents function f.
function g is an exponential function passing through the points (3, -53) and (5, -41). which statement is true over the interval 3, 5?
a. the average rate of change of f is the same as the average rate of change of g.
b. the average rate of change of f is less than the average rate of change of g.
c. the average rate of change of f is greater than the average rate of change of g.
d. the average rates of change of f and g cannot be determined from the given information.

Explanation:

Step1: Calculate the average rate of change for function \( f \)

The formula for the average rate of change of a function \( y = f(x) \) over the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\).
For function \( f \) with \( a = 3\), \( b=5\), \( f(3)=59\), \( f(5)=71\).

$$ \frac{f(5)-f(3)}{5 - 3}=\frac{71 - 59}{2}=\frac{12}{2}=6 $$

Step2: Calculate the average rate of change for function \( g \)

For function \( g \) with \( a = 3\), \( b = 5\), \( g(3)=- 53\), \( g(5)=-41\).

$$ \frac{g(5)-g(3)}{5 - 3}=\frac{-41-(-53)}{2}=\frac{-41 + 53}{2}=\frac{12}{2}=6 $$

Answer:

A. The average rate of change of \( f \) is the same as the average rate of change of \( g \)