Questions: Based on the graph above, estimate to one decimal place the average rate of change from x=1 to x=3.

Transcript text: Based on the graph above, estimate to one decimal place the average rate of change from $x=1$ to $x=3$ $\square$

Solution

Step 1: Identify the Points

The points on the graph are $(x_1, f(x_1)) = (1, 0)$ and $(x_2, f(x_2)) = (3, 0)$.

Step 2: Use the Formula for the Average Rate of Change

The formula for the average rate of change over the interval $[x_1, x_2]$ is: \[ ext{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}\]

Step 3: Substitute the Values into the Formula

Substituting the values into the formula gives us: \frac{0 - 0}{3 - 1} = 0

The average rate of change of the function over the interval $[1, 3]$ is approximately 0.

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