UHS PreCalculus
Adaption of AP Calculus AB/BC 2012 Question 3
Name_________________________
Let f be the function whose graph consists of three line segments and a semicircle, as shown above.
1. Domain of f __________________ Range of f ___________________
2. For what interval(s) of x is f positive? ________________ Negative? __________________
3. For what interval(s) of x is f increasing? ___________________ Decreasing? _____________________
4. For what value(s) of x is f(x)=0?
5. Calculus (specifically, Calculus I) is all about slope, or rate of change.
Considering only the three line segments, for which interval(s) of x is the average rate of change (slope) of f
positive? ____________________
Considering only the three line segments, for which interval(s) of x does f have an average rate of change −2?
____________________
6. On the graph above, draw the graph of |𝑓(𝑥)|. Let’s call this new graph 𝑔(𝑥).
For which values of x is g increasing? ____________________ Decreasing? _______________________
7. While Calculus I is all about slope, Calculus II is all about area. Connect the endpoints of the original graph to
the x-axis. Now find the “area under the curve” (i.e., the area made with the function and the x-axis) using
geometry formulas. Remember that if the graph is above the x-axis, you have positive area; if the graph is
below the x-axis, you have negative area.
UHS PreCalculus
Adaption of AP Calculus AB/BC 2011B Question 5
Ben rides a unicycle back and forth along a straight east-west track. The table above gives values for Ben’s velocity,
𝑣(𝑡), measured in meters per second, at selected times t.
1. Use the data to find the average rate of change of v from 𝑡 = 0 to 𝑡 = 60 seconds; indicate units of measure.
What do we call the rate of velocity?__________________________ Ask a student in physics if you don’t know.
2. Estimate total distance that Ben traveled between 0 seconds and 60 seconds by using a left Riemann sum
with three subintervals; include the units of your result.
3. Estimate total distance that Ben traveled between 0 seconds and 60 seconds by using a right Riemann sum
with three subintervals; include the units of your result.
4. Estimate total distance that Ben traveled between 0 seconds and 60 seconds by using a trapezoidal sum
with three subintervals; include the units of your result.