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.

The average rate of change is _____.

(1 point)
Responses

-2
-2

-1
-1

1
1

2
2
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Answer 1

To calculate the average rate of change of the function \( y = 3x + 2 \) 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, let \( a = -2 \) and \( b = -1 \).

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

2. Calculate \( f(-1) \): \[ f(-1) = 3(-1) + 2 = -3 + 2 = -1 \]

3. Now, substitute these values into the average rate of change formula: \[ \text{Average Rate of Change} = \frac{f(-1) - f(-2)}{-1 - (-2)} = \frac{-1 - (-4)}{-1 + 2} = \frac{-1 + 4}{1} = \frac{3}{1} = 3 \]

So, the average rate of change is \( 3 \), but none of the provided responses list \( 3 \). Therefore, it seems there may be an error in the options provided for the calculation.