Use the formula f(b)−f(a)b−a

Question

to calculate the average rate of change over the interval [−2,2]
given the function table for f(x)=2x+1


x f(x)
-2 0.5
-1 1
0 2
1 4
2 8(1 point)

Answer 1

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

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

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

1. First, we need to evaluate \( f(-2) \) and \( f(2) \):

   • From the table, \( f(-2) = 0.5 \)
   • From the table, \( f(2) = 8 \)

2. Now, substitute these values into the formula: \[ \text{Average rate of change} = \frac{f(2) - f(-2)}{2 - (-2)} = \frac{8 - 0.5}{2 + 2} = \frac{8 - 0.5}{4} = \frac{7.5}{4} \]

3. Simplifying \( \frac{7.5}{4} \): \[ \frac{7.5}{4} = 1.875 \]

Thus, the average rate of change of the function \( f(x) = 2x + 1 \) over the interval \([-2, 2]\) is \( 1.875 \).