Answered

What is the average rate of change of f(x), represented by the table of values, over the interval [-2, 3]?
x    f(x)

-6  2.5

-2  2.5

0      2

2      0

3      5



answers:

A5
B2.5
C1
D0.5

Verified Answer :

nobillionaireNobley

Average rate of change = (f(b) - f(a))/(b - a) = (f(3) - f(-2))/(3 - (-2)) = (5 - 2.5)/(3 + 2) = 2.5/5 = 0.5

Answer:

D. 0.5

Step-by-step explanation:

We will use average rate of change to solve our given problem.

\(\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}\)

The average rate of change between -2 and 3 would be:

\(\text{Average rate of change}=\frac{f(3)-f(-2)}{3--2}\)

Upon looking at our given table we can see that \(f(3)=5\) and \(f(-2)=2.5\).

\(\text{Average rate of change}=\frac{5-2.5}{3+2}\)

\(\text{Average rate of change}=\frac{2.5}{5}\)

\(\text{Average rate of change}=0.5\)

Therefore, the average rate of change over closed interval \([-2,3]\) is 0.5 and option D is the correct choice.

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