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

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

Here, \( a = -2 \) and \( b = -1 \). We need to find \( f(-2) \) and \( f(-1) \).

From the given function, we have:

\[ f(-2) = 3(-2) + 2 = -6 + 2 = -4 \] \[ f(-1) = 3(-1) + 2 = -3 + 2 = -1 \]

Now, we can substitute these values into the average rate of change formula:

\[ \text{Average Rate of Change} = \frac{f(-1) - f(-2)}{-1 - (-2)} = \frac{-1 - (-4)}{-1 + 2} \]

Calculating the numerator and denominator:

\[ = \frac{-1 + 4}{1} = \frac{3}{1} = 3 \]

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

\[ \boxed{3} \]