Question

3
select the correct answer.
the table represents function f.

x	3	4	5	6	7	8	9
f(x)	59	63	71	87	119	183	311

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 rates of change of f and g cannot be determined from the given information.
c. the average rate of change of f is less than the average rate of change of g.
d. the average rate of change of f is greater than the average rate of change of g.
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Explanation:

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

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

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

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

For \( g \), \( a = 3 \), \( b = 5 \), \( g(3) = -53 \), \( g(5) = -41 \). Using the same formula:

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

Answer:

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