Average Rate of Change Assessment
Name: __________________________
Pre-Calculus 1
[Level 4 – can identify increasing and decreasing intervals and calculate average rate of change]
State the intervals over which the function is increasing, decreasing and/or constant.
1.
2.
Increasing:
Increasing:
Decreasing:
Decreasing:
Constant:
Constant:
Calculate the average rate of change of the below functions over a given interval.
If it’s a context question, provide a clear, complete sentence context answer.
1. Two cars travel for 5 hours along Interstate 5. A South Dakotan in a 1983 Chevy Caprice travels
300 miles, always at a constant speed. A Californian in a 2009 Porsche travels 400 miles, but at
varying speeds (see graph to the right).
a. Compute the average velocity of each car
over the 5-hour trip. Remember that velocity
is distance over time.
b. Does the Californian drive faster than the South Dakotan over the ENTIRE 5 hour
interval? Justify your answer!
2.
What does this mean in context?
3. 𝑓(𝑥) = 2𝑥 2 − 2𝑥 − 1
3
𝑜𝑣𝑒𝑟 [ 1 , 2 ]
4. The police have accused a driver of breaking the speed limit of 60 miles per hour. As proof, they
provide two photographs. One photo shows the driver's car passing a toll booth at exactly 6 PM.
The second photo shows the driver's car passing another toll both 31 miles down the highway at
exactly 6:30 PM. Does the photo evidence prove that the driver broke the speed limit during this
time? Explain your reasoning with details.