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 1/3
-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 given formula:

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

Here, \( a = -2 \) and \( b = -1 \).

Let's first find \( f(-2) \) and \( f(-1) \).

From the table, we see:

• \( f(-2) = 1 \)
• \( f(-1) = 3 \)

Now substituting in the formula:

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

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

\[ \boxed{2} \]