Questions: Use the graph of (f(x)) to evaluate the following: The average rate of change of (f) from (x=1) to (x=3) is (square) Give your answer as an integer or reduced fraction.

$Use the graph of (f(x)) to evaluate the following: The average rate of change of (f) from (x=1) to (x=3) is (square) Give your answer as an integer or reduced fraction.$

Transcript text: Use the graph of $f(x)$ to evaluate the following: The average rate of change of $f$ from $x=1$ to $x=3$ is $\square$ Give your answer as an integer or reduced fraction.

Solution

Solution Steps

Step 1: Identify the coordinates

From the graph, identify the coordinates of the points where $ x = 1 $ and $ x = 3 $.

At $ x = 1 $, $ f(x) = 2 $. So, the point is (1, 2).
At $ x = 3 $, $ f(x) = 5 $. So, the point is (3, 5).

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

Substitute $ a = 1 $, $ b = 3 $, $ f(a) = 2 $, and $ f(b) = 5 $ into the formula: \[ \text{Average rate of change} = \frac{5 - 2}{3 - 1} = \frac{3}{2} \]