Use the formula f(b)−f(a)b−a

Question

to calculate the average rate of change over the interval [−2,−1]
given the function table for y=3x+2
. Express your answer as an integer.

x f(x)

−3
13

−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 \( f(x) = 3x + 2 \) over the interval \([-2, -1]\), we can use the formula:

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

In this case, \( a = -2 \) and \( b = -1 \).

We first need to find \( f(-2) \) and \( f(-1) \):

1. From the function table:
   • \( f(-2) = 1 \)
   • \( f(-1) = 3 \)

Now, we can substitute these values into the formula:

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

Calculating each part:

\[ f(-1) - f(-2) = 3 - 1 = 2 \] \[ b - a = -1 - (-2) = -1 + 2 = 1 \]

Now substitute these results back into the formula:

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

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

\[ \boxed{2} \]