Questions: Use the graph of f(x) to evaluate the following: The average rate of change of f from x=3 to x=5 is □ Give your answer as an integer or reduced fraction.

$Use the graph of f(x) to evaluate the following: The average rate of change of f from x=3 to x=5 is □ Give your answer as an integer or reduced fraction.$

Transcript text: Use the graph of $f(x)$ to evaluate the following: The average rate of change of $f$ from $x=3$ to $x=5$ is $\square$ Give your answer as an integer or reduced fraction.

Solution

Solution Steps

Step 1: Identify the points on the graph

From the graph, identify the points corresponding to $ x = 3 $ and $ x = 5 $.

At $ x = 3 $, $ f(x) = 5 $.
At $ x = 5 $, $ f(x) = 2 $.

Step 2: Use the average rate of change formula

The average rate of change of a function $ f(x) $ from $ x = a $ to $ x = b $ is given by: \[ \text{Average rate of change} = \frac{f(b) - f(a)}{b - a} \]

Step 3: Substitute the values into the formula

Substitute $ a = 3 $, $ b = 5 $, $ f(3) = 5 $, and $ f(5) = 2 $ into the formula: \[ \text{Average rate of change} = \frac{f(5) - f(3)}{5 - 3} = \frac{2 - 5}{5 - 3} = \frac{-3}{2} \]