Name: ______________________ Date: ______________________ Section: ____________
Review: (Unit III Lessons 5-9)
Compare Properties of Functions: Lesson 5
1. For the first leg of the Ramirez family’s trip, their speed averages 68 miles per hour. The second leg is
shown in the graph. Compare the speeds for each part of their trip.
2. The late fees for a school library are represented by the function c = 0.25d, where c is the total cost and d is
the number of days a book is late. The fees charged by a city library are shown in the table.
a.) Compare the functions’ y-intercepts and rates of change.
b.) Shamar checks out one book at each library and returns both books 3 days late. What are the late
fees for each library?
3. Matt and Seth purchase baseball cards each week. The amount of cards they each have in their collection
is shown in the graph and table. Who will have more cards in Week 20? Justify your response.
Construct Functions: Lesson 6
4. A teacher read part of a book to a class. The graph shows the number of pages read by the teacher over
the next several days. Find and interpret the rate of change and the initial value.
5. A water park charges a rental fee plus $1.50 per hour to rent inflatable rafts. The total cost to rent a raft
for 6 hours is $15. Assume the relationship is linear. Find and interpret the rate of change and the initial
value.
6. Melissa frosted some cupcakes in the morning for a party. The table shows the total number of cupcakes
frosted after she starts up after lunch. Assume the relationship between the two quanitites is linear. Find and
interpret the rate of change and the initial value.
Linear and Nonlinear Functions: Lesson 7
Determine whether each table represents a linear or nonlinear function. Explain.
7.
8.
9. The area of a square is a function of its perimeter. Graph the function on a separate sheet of grid paper.
Explain whether the function is linear and if the graph is increasing or decreasing. Use a separate sheet of
graph paper.
Quadratic Functions: Lesson 8
Graph each function.
10.
11.
12.
13. Alexis is making a photo frame. The width of the frame is x inches, and the length of the board is (x + 2)
inches.
a.) Write a function that represents the area, A, of the frame.
b.) Graph the function using a separate sheet of paper. (Hint: make a table first)
c.) If the width of the frame is 4 inches, what is its area?
14. Circle the more narrow quadratic graph. Explain.
a.) y = x2
b.) y = -6x2 – 2
c.) y = 4x2 + 1
d.) y = -x2 + 6
15. The quadratic equation 𝐴 = 6𝑥 2 models the area of a triangle with base 3x and height 4x. Graph the equation.
Explain why you only need to graph the function in the upper right quadrant.
Without graphing, determine whether each equations represents a linear function, quadratic function, or
niether.
16. y = x2
17. y = 8
18. x = 5
19. y = x2 + 3x + 12
20. y = 3(x -4)
Qualitative Graphs: Lesson 9
21. The graph below displays the height of an airplane. Describe the change in the airplane’s height over
time.
22. Jamaal purchased the same number of action figures daily for one week. Over the next week, he sold
most of them on the Internet. Sketch a qualitative graph to represent the situation.