Question

Use the formula f(b)−f(a)/b−a to calculate the average rate of change over the interval [−2,−1] given the function table for y=3^x+2 . Express your answer as an integer.

x f(x)
−3 1/3
−2 1
−1 3
0 9
(1 point)
The average rate of change is _
.

Answer 1

To calculate the average rate of change of the function \( f(x) = 3^x + 2 \) over the interval \([-2, -1]\), we will use the formula:

\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]

where \( a = -2 \) and \( b = -1 \).

From the table, we find the function values:
- \( f(-2) = 1 \)
- \( f(-1) = 3 \)

Now, substituting these values into the formula:

\[
\text{Average Rate of Change} = \frac{f(-1) - f(-2)}{-1 - (-2)}
\]

This simplifies to:

\[
\text{Average Rate of Change} = \frac{3 - 1}{-1 + 2} = \frac{2}{1} = 2
\]

Thus, the average rate of change over the interval \([-2, -1]\) is:

\[
\text{The average rate of change is } 2.
\]