Name __________________________________________ Class _____________________ Date ____________________
Unit 1 Test Review
Solve each equation. Check your solution.
1. –5a + 54 = 5(–4a + 13.89)
2. 14 + 3n = 8n – 3(n – 4)
3. –(3z + 4) = 6z – 3(3z + 2)
Write and solve an equation for each situation.
4. Shirley is going to have the exterior of her home painted. Tim’s Painting charges $250 plus $14 per hour.
Colorful Paints charges $22 per hour. How many hours would the job need to take for Tim’s Painting to be
the better deal?
5. Three times the sum of a number and 4 is 8 less than one-half the number. Write and solve an equation to find the
number.
Solve each inequality. Graph the solution on a number line.
6. 53 > 3(3z + 3) + 3z
7. 2(6 + s) < 16 + 2s
8. 3v  12 > 5v + 10
9. 8 ≤ c – 17 < 35
10. 4  y + 2  3(y  2) + 24
11. 3d + 3  1 or 5d + 2  12
12. A family decides to rent a boat for the day while on vacation. The boat’s rental rate is $500 for the first two
hours and $50 for each additional half hour. Suppose the family can spend $700 for the boat. What inequality
represents the number of hours for which they can rent the boat?
13. Explain how the vertical line test can be used to determine if a relation is a function.
14. Explain when a relation is not a function.
15. Describe the relationship between relation, domain, and range.
16. Given a table of points for x and y, explain how to determine if the relation is a function.
Identify the domain and range of each relation.
17. {(5, –4), (3, –5), (4, –3), (6, 4)}
18. {(0.3, 0.6), (0.4, 0.8), (0.3, 0.7), (0.5, 0.5)}
19.
20.
21.
22.
Use the functions f(x) = 3x + 2 and g(x) = x2 – 4 to find the value of each expression.
23. 𝑓(3) + 𝑔 (4)
24. 𝑓(3) − 2 ∙ 𝑔 (1)
25. 𝑔 (𝑓(3))
26. 𝑓(𝑥 + 2)
27. 𝑓(3𝑥) − 1
28. 𝑓(𝑦 − 1) + 𝑔 (𝑦)
Find the range of each function given the domain.
29. 𝑓(𝑥) = – 2𝑥 + 5; {–2,–1,0,1,2}
30. 𝑓(𝑥) = 𝑥 2 + 2; {–1,–0.5,0,0.5,1}
Find a reasonable domain and range for the following situation.
31. A high school is having a pancake breakfast fundraiser. They have 3 packages of pancake mix that each feed 90
people. The function N(p) = 90p represents the number of people N(p) that p packages of pancake mix feed.
32. Reasoning. If f (x) = x2– 3 and f (a) = 46, what is the value of a? Explain.
Determine whether each equation represents direct variation. If it does, find the constant of variation.
33. –7x = –56y
34. 3y + 2 = 2x
Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y
when x = 8.
35. y = 3 when x = 8
36. y = 7.92 when x = 2.2
37. y = –21 when x = 7
Tell whether the two quantities vary directly. Explain your reasoning.
38. Sara makes $3.50 more per hour than Pasco.
39. Jasmine scores 10 points per game.
For the data in each table, tell whether y varies directly with x. If it does, write an equation for the direct variation.
40.
41.
42. The perimeter of a square varies directly with the length of one side. What is an equation that relates the perimeter p
and length l of the side? What is the graph of the equation?