Ch. 1 Pretest
Quantities & Relationships
Name ______________________________
Period _________
Show all of your work on a separate sheet of paper!
Identify the independent quantity and the dependent quantity in each scenario.
1. Hector knows there is a relationship between the number of cakes he bakes and the time it takes
him to bake those cars. Identify the independent quantity and the dependent quantity.
2. Jason is walking to the mall and he knows that he can walk at a rate of 5 miles per hour.
Identify the independent quantity and the dependent quantity.
3. The height of a tomato plant is recorded daily for 2 weeks.
Identify the independent quantity and the dependent quantity.
4. A baker spends $6 on ingredients for each cake he bakes.
Identify the independent quantity and the dependent quantity.
Sketch and label a graph for each scenario.
5. Kyle is filling his backyard pool to get ready for the summer. He is using a garden hose to fill the
pool at a rate of 14 gallons per minute.
6. Jessika is training to participate in competitive trampoline. In her best jump, she can reach a
maximum height of about 9 meters and can spend about 2 seconds in the air performing tricks.
7. Each day Marisa starts her walk to school at 7:30 am. At 7:35 am she stops at her friend Zoey's
house. Zoey is usually late and Marisa must wait at least 5 minutes for her to get ready. At 7:40 am
Marisa and Zoey leave Zoey's house and arrive at school at 7:50.
8. Explain the difference between a continuous graph and a discrete graph. Sketch a graph of each.
Explain why these graphs may have been grouped together.
9.
10.
11.
12.
Rewrite each function using function notation.
13. Rewrite 𝑦 = 4𝑥 + 15 so that the dependent quantity, defined as 𝑀, is a function of the
independent quantity 𝑥.
14. Rewrite 𝑦 = 𝑘 2 − 3𝑘 so that the dependent quantity, defined as 𝐿, is a function of the independent
quantity 𝑘.
Determine if each graph represents a function. Why or why not?
15.
16.
17.
18.
Determine whether each graph represents an increasing function, a decreasing function, a
constant function, or a combination.
19.
20.
21.
22.
Sketch two different graphs of each function family.
23. Linear function
24. Quadratic function
25. Exponential function
26. Linear Absolute Value Function
27. Piecewise Function
Sketch a graph for each with the given characteristics.
28. Is a smooth curve, is continuous, has a minimum, and is quadratic.
29. Is linear, is discrete, and is decreasing.
30. Is a smooth curve, is increasing, is continuous, and is exponential.
31. Has a maximum, is continuous, and is a linear absolute value function.
32. Is linear, is continuous, is neither increasing nor decreasing, and does not pass through the origin.
33. Is discrete, has a maximum, does not pass through the origin, and is quadratic.
Write a scenario that best describes what is happening in the graph.
34.
Decide what function family each of the following equations belong to.
2
35. 𝑓(𝑥) = |4𝑥 − 1| + 2
36. 𝑓(𝑥) = −2𝑥 + 1
37. 𝑓(𝑥) =
38. 𝑓(𝑥) = 𝑥 2 + 3𝑥 + 2
39. 𝑓(𝑥) = 3𝑥
40. 𝑓(𝑥) = 5 𝑥
Evaluate the following expressions.
𝟏
𝟑
𝟑
𝟒
41. − −
𝟏
𝟑
43. − (− )
𝟒
𝟓
45.
0
42.
44.
𝟓
𝟒
46.
8
Simplify each of the following expressions.
47.
(6−8)2
56÷4∗2
48. (1 + 23 ) − 75 + 25 ÷ 5
49.
8
2
∙ 5(1 − 4) + 6
𝟏
𝟐
𝟓
𝟑
− +
÷
4
0
𝟗
𝟑
3
𝑥+1