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

Solution Steps

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.

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

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

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