Pre-Test Unit 8: Piecewise Functions KEY
You may use a calculator for the whole test.
Fill out an / chart and graph each of the following functions. (5 pts; 2 pts for appropriate inputs, 1 pt for
correct outputs, 2 pts for graphing correctly)
1. | 5| 7
7
5
6
6
5
7
2 4; 2
3. 3; 2
6
8
2
2
5
6
0
3
4
4
2
4
4
6
3
5
2. 2 4
2
4
4. 3
2
4
5
2
0
6
6
1.5
4
1
6
2; 0.5
6
4
4 8; ! 4
4
4
4
8
2
1
5
7
0
8
0
2
6
4
2
5
7
1
4
8
8
8
Given that " is the parent function, describe the transformation of #. (5 pts; partial credit at teacher
discretion)
5. ||
& | 6| − 8
6. & = − 3 + 5
Translate left 6, down 8
Translate right 3, up 5
Reflect across -axis
8. = ||
& = −3||
9. = $%
& = 5$%
10. = & = 5
Steps 5 times taller
Steps 5 times thinner
Reflect across -axis, steeper slope
7. $%
& = −$%
Solve the following equations. (5 pts; 3 pts for appropriate work, 2 pts for solution)
11. | 9| 4
No solution
13. 2| + 3| = 8
= −7, = 1
12. + 5 = 10
5≤<6
14. = 3 where =
= 3.5, = 6, = 9
2 − 4; < 4
+ 6; 4 ≤ ≤ 8
− 6; > 8
(− Solve the following equations. (5 pts; 3 pts for appropriate work, 2 pts for solution)
12 < ≤ 13
+ 2 + 4; ≤ 0
16. = 8 where = )
−3 + 5; > 0
= −4, = 0
17. | − 3| < 15
18. |2 + 7| ≥ 11
15. $ 7% = 6
−12 < < 18
≤ −9 or ≥ 2
Create a function to model the following situations. (5 pts; partial credit at teacher discretion)
19. You decide to rent a luxurious cabin out in the woods. However, due to high demand in the area, they force
to rent the cabin in chunks of 5 days. In other words, if you stays one day, two days, three days, four days, or five
days, it will all cost the same amount. The cabin company charges $3000 for every chunk of 5 days.
1
+, = 3000 - ,.
5
20. A manufacturer produces tennis balls. To be a legal tennis ball to use in USTA tournaments, the diameter of
ball must be within 0.1+/ of the mandated 6.7+/.
|, − 6.7| ≤ 0.1
Unit 8 Homework Key
Lesson 8.1
Fill out an / chart and graph each of the following functions.
2. & | 2|
1. ||
4
2
2
1
0
0
2
1
4
2
4. | 4| 5
2
7
3
6
4
5
4
& 2
3
1
3. 0 || 4
2
0
1
1
0
2
6
7
2
& 0
1
2
0
4
1
5
0
1
2
4 5 6
5. & 2|| 4
5
6
2
0 6
1
2
2
0
6. 0 | 1|
5
0 2
2
1
1
0
4
7
1 2
Given that " || is the parent function, describe the transformation of #.
7. & | 3| 2
8. & | 4|
9. & 2|| 6
Translated right 3 units and
up 2units
Reflected across -axis and
translated left 4 units
Stretched 2 times closer to 1-axis
and translated down 6 units
10. & | 2| 7
11. & ||
12. & | 1| 5
Translated right 2 units and
Up 7 units
Stretched half as close to 1-axis
and reflected across -axis
Stretched as close to 1-axis and
translated right 1 unit, up 5 units
Solve the following equations.
13. | 3| 6
14. 2|| 5 9
15. | 5| 2 7
16. | 2| 10 4
17. 2| 7| 3 15
18. || 4 24
3, 9
8, 4
Solve the following inequalities.
32
10, 0
1, 13
no solution
19. | 2| 4
20. | 4| 1 0
21. 2|| 3 3
22.
3 3
23. 2| 3| 5 1
24. | 6| 2 3
5
6; 2
1
35
|
5| 1
7; 3
57
Set-up an absolute value inequality to model each of the following situations.
25. On the MAP test you originally scored a 272. To validate your high test score, the school wants you to retake
the test. According to the MAP test guidelines, you should score within 3 points of your original score on a retake.
| − 272| ≤ 3
26. A factory produces cereal boxes that are supposed to be 12 inches high, but there is an acceptable margin of
error of 0.1 inch.
| − 12| ≤ 0.1
27. The correct answer to a system of linear equations is the point 2.8, −3.2, but the teacher says your estimate
can be within half a unit for both coordinates. (Note: You need to set-up two absolute value inequalities - one for
the -coordinate and one for the 1-coordinate.)
| 2.8| ≤ 0.5
|1 + 3.2| ≤ 0.5
28. A couple invites 300 people to their wedding knowing that all of them may not show-up and that some
people invited may bring along extra people. To plan for such an event, they decide to include of margin of error
of 20 people when they talk to the caterer.
| − 300| ≤ 20
Lesson
Lesson 8.2
Fill out an / chart and graph each of the following functions.
1. 0
0
0.5 1 1.5
0 0.5 0.5
4. 4 5 3
2
2
1
3
0
3
1
4
2
1
2
4
2. & 2
2 1.5 1 0.5 0
& 0
0
1 1 2
5. & $% 4
2 1.5
& 2 2
1 0.5 0
3 3 4
3. 0 2 4
0 0.25 0.5 0.75 1
0 4 4 3 3 2
6. 0 $ 1%
0
0
1
3
0.5
0
1
0
1.5
2
1
1
3
3
Given that " is the parent function, describe the transformation of #.
7. & 6 27
Translated left 2 units and
steps are longer
8. & 4
Reflected across -axis and
translated up 4 units
9. & 6
Reflected across 1-axis
and translated right 6 units
Given that " $% is the parent function, describe the transformation of #.
10. & 2$% − 7
Stretched 2 times farther from
-axis and translated down 7 units
11. & = −$4%
12. & = − + 1 + 5
Steps are shorter
and reflected across -axis
Reflected across 1-axis and
translated left 1 unit, up 5 units
13. 2 = 10
14. 4 + 5 = 4
15. 6 − 17 + 4 = 0
16. $−4% − 9 = −5
17. −$ − 5% = 15
18.
Solve the following equations.
5≤<6
−1 ≤ < − 8
−5 ≤ < −4
−11 < ≤ −10
−6 ≤ < −4
4
+ 5 = 8
22 < ≤ 231/2
Create a function to model the following situations.
19. You want to bring cupcakes to school for your birthday. Each case comes with 12 cupcakes and costs $6.95.
Create a function that models the number of cases you should buy in terms of the number of students in your class.
1
9: = 6.95 - :.
12
20. Renting jet skis in the Bahamas costs $40 per hour plus a $15 gas fee. Create a function that models the cost
in terms of the number of hours the jet skis were rented.
9ℎ = 40$ℎ% + 15
21. Laser tag at Fred’s Family Fun costs $6 for every segment of 15 minutes of play, plus a $5 battery fee. Create
a function that models the cost in terms of the number of minutes playing tag.
1
9/ = 6 - /. + 5
15
22. A textbook company charges $725 for each case of books that it sells. A case can contain any number of
books up to 30 books. They charge a flat shipping fee of $100. Create a function that models the cost in terms of
the number of books needed.
1
9; = 725 - ;. + 100
30
23. Long distance phone calls cost $0.99 for the first minute, and $0.39 for every minute after that. Create a
function that models the cost in terms of the duration of the phone call in minutes.
9/ = 0.39$/ − 1% + 0.99
24. You’re ordering pizza for your birthday party. You estimate that each pizza will serve 4 people. Create a
function that models the number of pizzas you need to order in terms of the number of people attending.
1
<= = - =.
4
Lesson 8.3
Fill out an / chart and graph each of the following piecewise functions.
1. 5; ! 3
2 9; 3
3
4
7
5
3. 0
5
6
3
3
6
5
1
5; 0
2; ! 0
8
9
0
2
6
8
1
1
4
7
2
0
6
7
4
1
2
6
3
1
9
8
3
3
0
5
4
2
2. )
2
4
2
5
4. 2; 2
3 6; 2
1
2
3
6
0
0
4
5
2 15; 1
2
5
2
6
> 1;6 4; 6
10
5
6
3
6
1
9
3
3
2
7
1.5
8
1
0
1
8
2
2
4
6
3
6
7
1
3
0
9
2.5
6
3
6
1
10
3
4; 8 12; 2
5. (
8;2 2
8 12; ! 2
6
0
2
8
2
0
5
3
1
8
3
3
4
4
0
8
4
4
3
3
1
8
5
3
2
0
2
8
6
0
6. > 7;2 2
4; 2
10
1
2
3
2
3
8
0
1
6
4
2
6
1
0
7
6
1
Solve the following equations.
2 5; 5
7. 3 where 4; 5
2
3 1; 5
9. 2 where )
1; 5
no solution
2
8. 4 where )
2, 1
4
2
1
6
8
0
2
3
2
3
10
1
4 8; ! 0
2 4; 0
5; 1
10. 4 where (2 10; 1 6
2; 6
2, 3
3 3; 1
3 5; 8
4 5;1 512. 7 where ? 2 3;8 5
11. 0 where (
4; 5
3 9; 5
1, 5
5, 7
Review Unit 8: Piecewise Functions KEY
Fill out an / chart and graph each of the following functions.
You may use a calculator.
1. | 3| 4
1
6
2
5
3. 3$ 5%
3
6
3.5
3
3
4
4
3
4
5
4.5
0
5
6
5
0
2. 2|| 6
2
2
1
4
4. 6 7 6
2
7
1
7
0
6
1
4
2
2
0
6
1
6
2
5
5. 2 10; 6
5; ! 6
10
10
6
3
9
8
3
4
8
6
0
5
7
4
3
6
6. 6
2
6
7
4 5; 4
3; 4
0
5
4
5
1
8
6
6
Given that " is the parent function, describe the transformation of #.
7. ||
& | 4| 1
Translate right 4, up 1
10. $%
& $ 4%
Reflect across 1-axis
translate left 4
8. ||
& | 5|
8 2
3
8
10
8
4
5
12
9
9. $%
& 2$% 3
Reflect across -axis
translate left 5 units
Steps 2 times farther from -axis
translate up 3
11. 12. & & 8 5
6 7
Steps 3 times longer
Steps 4 times closer to -axis
translate down 5
Solve the following inequalities.
13. 2| 3| 10
2
9
8
7
14. @ 2@ 1
3, 9
Solve the following equations
15. | 2| + 6 = 12
16. 2 + 3 = 7
= −4, 8
2 ≤ < 2.5
17. 2|| + 8 = 2
18. = −1 where =
no solution
=4
19. $ 2% + 4 = 9
20. = 8 where = 6<≤7
21.
$% +
= −6, = −2, = 8
− 1; < −3
+ 1;−3 ≤ ≤ 3
(− − 3 − 5; > 3
2 + 4 ; ≤ 0
8
+ 6; > 0
22. − + 5 = −8
7=3
−9 < ≤ −8
12 < ≤ 13
Create a function to model the following situations.
23. General Mills produces boxes of cereal. According to regulations, the amount of the cereal in each box must
be within 0.07 ounces of the amount listed, which is 20.5 ounces.
|+ − 20.5| ≤ 0.07
24. At Blaine’s Bowling Lanes, cosmic bowling costs $4 for each hour segment and an additional $2 for shoes.
Create a function that demonstrates the cost in terms of the number of hours spent bowling.
+ℎ = 4$ℎ% + 2
25. A newly engaged couple is ordering cakes for their wedding reception. Each cake serves 12 people. Create a
function that demonstrates the number of cakes they should order based on the number of people planning to
attend.
+A = -
1
A.
12