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
x. f(x).
-3 1/3
-2 1
-1 3
0 9

Responses:
3.
6.
2.
2/3.

Answer 1

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

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

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

Now we need to find \( f(-2) \) and \( f(-1) \) using the values given in the table:

• From the table, we see that:
  • \( f(-2) = 1 \)
  • \( f(-1) = 3 \)

Now we can substitute these values into the formula:

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

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

\[ \boxed{2} \]