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=3^x^+^2
. Express your answer as an integer.
graph catogories, x, f (x)
x, -3, -2, -1, 0
f (x), 1/3, 1, 3, 9
The average rate of change is _____.

(1 point)
Responses

1
1

-1
-1

-2
-2

2

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:

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

Given \( a = -2 \) and \( b = -1 \):

1. First, we find \( f(-2) \) and \( f(-1) \) from the table:

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

2. Now, we 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 is \( \boxed{2} \).