Questions: Based on the graph above, estimate (to one decimal place) the average rate of change from x=1 to x=5.

Based on the graph above, estimate (to one decimal place) the average rate of change from x=1 to x=5.
Transcript text: Based on the graph above, estimate (to one decimal place) the average rate of change from $x=1$ to $x=5$. $\square$
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Solution

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Solution Steps

Step 1: Identify the coordinates at \( x = 1 \) and \( x = 5 \)

From the graph, observe the y-values at \( x = 1 \) and \( x = 5 \):

  • At \( x = 1 \), the y-value is approximately 4.
  • At \( x = 5 \), the y-value is approximately 0.
Step 2: Calculate the change in y-values

Subtract the y-value at \( x = 1 \) from the y-value at \( x = 5 \): \[ \Delta y = y(5) - y(1) = 0 - 4 = -4 \]

Step 3: Calculate the change in x-values

Subtract \( x = 1 \) from \( x = 5 \): \[ \Delta x = 5 - 1 = 4 \]

Step 4: Compute the average rate of change

Divide the change in y-values by the change in x-values: \[ \text{Average rate of change} = \frac{\Delta y}{\Delta x} = \frac{-4}{4} = -1 \]

Final Answer

The average rate of change from \( x = 1 \) to \( x = 5 \) is \(-1\).

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