Problem

Calculate the average rate of change of the function f(x)=2x+3 between the points (1,f(1)) and (3,f(3)).

Answer

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Answer

Finally, we calculate the average rate of change, which is the difference in the y-coordinates divided by the difference in the x-coordinates: f(3)−f(1)3−1=42=2.

Steps

Step 1 ：First, we need to calculate the y-coordinate for each point. We substitute x into f(x) to get f(1)=2(1)+3=5 and f(3)=2(3)+3=9.

Step 2 ：Then, we find the difference in the y-coordinates of these two points, which is f(3)−f(1)=9−5=4.

Step 3 ：Next, we find the difference in the x-coordinates of these two points, which is 3−1=2.

Step 4 ：Finally, we calculate the average rate of change, which is the difference in the y-coordinates divided by the difference in the x-coordinates: f(3)−f(1)3−1=42=2.

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