4-9 Linear Functions Test Review Unit 4 Linear Functions ...
Tanks a Lot Introduction to Linear Functions Vocabulary 1 ......2011/10/31 · Slope-Intercept Form...
Transcript of Tanks a Lot Introduction to Linear Functions Vocabulary 1 ......2011/10/31 · Slope-Intercept Form...
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Skills Practice Skills Practice for Lesson 1.1
Name _____________________________________________ Date ____________________
Tanks a Lot Introduction to Linear Functions
Vocabulary Define each term in your own words.
1. function
2. linear function
3. independent variable
4. dependent variable
5. variable
Problem Set Determine the independent quantity and the dependent quantity in each example.
1. A car is traveling at a rate of sixty miles per hour for several hours.
independent quantity: time in hours
dependent quantity: distance in miles
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2. Sharon is growing at a rate of two inches per year.
3. The area of a square floor is the product of the length of two of its sides.
4. The perimeter of a square is the sum of the length of all four of its sides.
5. The length of a video file in minutes relates to the size of the file in bytes.
6. The total weight of a bag of apples in pounds relates to the number of apples in
the bag.
Define a variable to represent each of the quantities. Then write an equation that shows the relationship between the two variables.
7. A runner travels 4 miles per hour. Write an equation to show the relationship
between the total distance the runner travels and the time.
Let t represent the amount of time in hours.
Let d represent the distance the runner travels in miles.
d � 4t
8. Each DVD at an electronics store costs $12.50. Write an equation to show the relationship
between the total cost when purchasing DVDs and the number of DVDs.
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9. To make one solar panel, a company uses two kilograms of silicon. The company
has 100 kilograms of silicon. Write an equation to show the relationship between
the amount of silicon remaining and the number of solar panels made.
10. A bowling ball company uses seven pounds of resin to make one seven-pound bowling
ball. They have a total of 490 pounds of resin. Write an equation to show the relationship
between the amount of resin remaining and the number of seven-pound bowling
balls made.
11. Julia opens a bank account and deposits $500 into the account. Each month, she
deposits $50 into the account. Write an equation to show the relationship between
the total amount of money in her bank account and the number of months since
she opened the account.
12. A water tower contains 15,000 gallons of water. Each week, 2500 gallons of water
are used and 1000 gallons of water are added. Write an equation to show the
relationship between the total amount of water remaining in the water tower and
the number of weeks that have elapsed.
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Graph each linear function.
13. y � 2 x � 1 14. y � 3x � 2
15. y � � 1 __ 2 x � 2 16. y � 2 __
3 x � 1 __
2
17. y � �4x � 5 __ 4 18. y � 2x � 7 __
3
1
2
3
4
–1
–2
–3
–4
y
1 3 42–3–4 –2 –1 x0
y = 2x – 1
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Use the given information to answer each question.
19. The distance, d, in miles that a plane travels can be modeled by the equation d � 550t,
where t represents the time in hours. If the plane travels for 7 hours, how far will it go?
d � 550t
d � 550(7)
d � 3850
The plane will travel 3850 miles in 7 hours.
20. The distance, d, in feet that a fly travels can be modeled by the equation
d � 5t, where t represents the time in seconds. If the fly travels for 30 seconds,
how far will it have gone?
21. The equation w � 1,000,000 � 20m shows the amount of water, w, in gallons
remaining in a water tower, where m represents the number of minutes that have
passed. When will there be 750,000 gallons of water in the water tower?
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22. The equation a � 1750 � 50t shows the amount of money, a, in dollars remaining
in a bank account where t represents the time in weeks. When will the balance in
the account be $1000?
23. A ticket seller’s weekly earning, s, in dollars can be modeled by the equation
s � 0.10t � 350, where t represents the number of tickets he sells. How many
tickets will the ticket seller have to sell to make $440 that week?
24. The total number of computers, c, that a company can manufacture can be
modeled by the equation c � 1 ___ 50
s � 250, where s represents the number of
screws that they need to order. How many screws will they need to order so that
they can manufacture 525 computers?
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Skills Practice Skills Practice for Lesson 1.2
Name _____________________________________________ Date ____________________
Calculating Answers Solving Linear Equations and Linear Inequalities in One Variable
Vocabulary Write the term that best completes each statement.
1. The solution of an inequality can be graphed on a(n) .
2. Adding, subtracting, multiplying, and distributing are all examples of
that can be used to solve an equation.
3. Addition, subtraction, multiplication, and division are the four
basic that can be applied to both sides of a linear equation to
solve the equation.
4. A(n) is a statement that compares two expressions.
Problem Set Indicate which transformation(s) are needed to solve each equation.
1. x � 1 � 4 2. x � 3 � 2
Add 1 to both sides.
3. 2x � 4 4. x __ 4 � 7
5. 3x � 2 � 8 6. x __ 2 � 5 � 15
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S olve each equation.
7. x � 3 � 10 8. �3 � x � 1
x � 3 � 3 � 10 � 3
x � 7
9. 2x � 6 � 10 10. 3x � 9 � 27
11. x __ 2 � 3 � 1 12. � x __
3 � 2 � 4
13. � 2 __ 3
x � 3 � �1 14. 3 __ 5 x � 4 � �8
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15. 2 x � 15 � 5 � 3x 16. 4x � 3x � 9 � 2 x
S olve each inequality. Graph the solution on a number line.
17. 3x � 2 � 8 18. 2x � 5 � 7
3x � 2 � 2 � 8 � 2
3x � 6
3x ___ 3 � 6 __
3
x � 2
19. �4x � 3 � �13 20. 2 � 3x � 11
21. 2x � 3 � 5 22. �x � 4 � �13
1 3 4 52–3–4–5 –2 –1 0
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23. 2( x � 3) � 5 24. 4 � �3(2x � 5)
25. � x __ 2
� 3 � 4 26. 2 __ 3 x � 4 � 10
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Skills Practice Skills Practice for Lesson 1.3
Name _____________________________________________ Date ____________________
Running a 10K Slope-Intercept Form of Linear Functions
Vocabulary Determine each of the following for the linear function 2 x � 3y � 6.
1. slope 2. y-intercept
3. slope-intercept form 4. x-intercept
Problem Set Identify the slope of each linear function.
1. y � 2 x � 3 2. y � �3x � 4
The slope is 2.
3. y � � 2 __ 3 x � 1 __
2 4. y � 5 __
2 x � 2 __
5
Identify the y-intercept of each linear function.
5. y � �5x � 2 6. y � x � 3
The y-intercept is 2.
7. y � 2 __ 3 x � 1 __
2 8. y � � 3 __
2 x � 3 __
2
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Write a linear equation in slope-intercept form for each situation.
9. Louise opens a bank account and deposits $250. Every month she deposits $50 into her
account. Write an equation to represent the amount she has in her account after x months.
y � 50x � 250
10. Erin opens a bank account and deposits $350. Every month she withdraws $25
from her account. Write an equation to represent the amount she has in her
account after x months.
11. A computer is downloading a 100-megabyte program file. It downloads the
program at a rate of 5 megabytes per minute. Write an equation to represent the
number of megabytes left to download after x minutes.
12. Marco has 20 gigabytes of computer programs on his computer. Every month he
adds 1.5 gigabytes of programs to his computer. Write an equation to represent the
number of gigabytes of programs he has on his computer after x months.
Calculate the slope and y-intercept for each function.
13. A linear function passes through the points (0, 0) and (4, 8).
The y-intercept is 0.
m � y2 � y1 _______ x2 � x1
� 8 � 0 ______ 4 � 0
� 8 __ 4 � 2
The slope is 2.
14. A linear function passes through the points (0, 0) and (3, �27).
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15. A linear function passes through the points (�4, 9) and (3, 5).
16. A linear function passes through the points (�5, �2) and (3, 10).
17. A linear function passes through the points (3, 0) and (4, 2).
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18. A linear function passes through the points (�2, �6) and (�4, 0).
Graph each linear function using its slope and y-intercept.
19. y � x � 2 20. y � �2x � 3
Slope � 1
y-intercept � 2
1
2
3
4
–1
–2
–3
–4
y
1 3 42–3–4 –2 –1 x
y = x + 2
0
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21. y � � 1 __ 2 x � 1 22. y � 3 __
2 x � 1
23. y � 4 24. y � �3
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Skills Practice Skills Practice for Lesson 1.4
Name _____________________________________________ Date ____________________
Pump It Up Standard Form of Linear Functions
Vocabulary Give an example of each key term.
1. standard form of a linear equation
2. slope-intercept form of a linear equation
Problem Set For each linear equation written in standard form, calculate the x- and y-intercepts. Use the intercepts to graph the equation.
1. x � y � 3 2. x � y � �2
x � 0 � 3 0 � y � 3
x � 3 y � 3
x-intercept � 3; y-intercept � 3
1
2
3 (0, 3)
(3, 0)
4
–1
–2
–3
–4
y
1 3 42–3–4 –2 –1 x0
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3. 2x � 3y � 6 4. x � 2y � 4
5. �2x � 5y � 10 6. 3x � 4y � 12
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7. 2 x � y � 3 8. �x � 3y � 5
Rewrite each linear equation in slope-intercept form.
9. x � y � 2 10. �x � y � �1
y � �x � 2
11. 2x � y � 5 12. 2 x � y � 3
13. 2x � 3y � 12 14. 5x � 3y � 15
15. �3x � 2y � 1 16. �x � 5y � 10
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Rewrite each linear equation in standard form.
17. y � 2 x � 3 18. y � �4x � 5
�2 x � y � �3
19. y � 1 __ 3 x � 4 20. y � � 2 __
3 x � 1
21. y � � 5 __ 4 x � 1 __
6 22. y � 4 ___
15 x � 5 __
9
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Skills Practice Skills Practice for Lesson 1.5
Name _____________________________________________ Date ____________________
Shifts and Flips Basic Functions and Linear Transformations
Vocabulary Write the term that best completes each statement.
1. A function undergoes a(n) when it is stretched or shrunk.
2. A(n) is a line in which a function is flipped so that it mirrors itself.
3. A(n) is a transformation in which a function is flipped over a given line.
4. The function y � x is the of the function y � 2 x � 3.
Problem Set Indicate the algebraic transformation which was performed on the basic function to result in each transformed function.
1. y � x � 2 2. y � x � 1
Add 2.
3. y � �4x 4. y � 1 __ 5 x
Indicate the graphical transformation(s) which were performed on the basic function to result in each transformed function.
5. y � x � 3
Move the graph down 3 units.
6. y � x � 1
7. y � 2 x � 3
8. y � �3x � 4
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9. y � � 1 __ 2 x � 3
10. y � 5 __ 3 x � 4
Graph each set of equations on the same grid. Compare the graphs of the lines. Then determine whether the graphs of the lines are parallel, perpendicular, or neither.
11. y � x � 3 and y � x � 1 12. y � 2 x and y � 4x
The first graph is shifted two units up from the second graph. The lines
are parallel.
1
2
3 y = x + 1
y = x + 3
4
–1
–2
–3
–4
y
1 3 42–3–4 –2 –1 x0
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13. y � �x and y � x � 2 14. y � 1 __ 2 x � 2 and y � �2x � 3
15. y � 2 __ 3 x � 2 and y � 2 __
3 x � 2 16. y � 1 __
4 x � 3 and y � 1 __
2 x � 1
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17. y � � 1 __ 5 x and y � 5x 18. y � �x � 2 and y � x � 2
19. y � �2 x � 1 and y � �2 x � 3. 20. y � 0 and y � 3
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Skills Practice Skills Practice for Lesson 1.6
Name _____________________________________________ Date ____________________
Inventory and Sand Determining the Equations of Linear Functions
Vocabulary Identify the similarities and differences between each pair of key terms.
1. point-slope form and two-point form
2. parallel lines and perpendicular lines
Problem Set Determine the slope-intercept form of the equation of each line.
1. Slope � 2 and y-intercept � 3 2. Slope � �4 and y-intercept � 10
y � 2 x � 3
3. Slope � �1 and y-intercept � �4 4. Slope � 1 and y-intercept � �12
Determine the slope-intercept form of the equation of each line.
5. Slope � �5 and the line passes 6. Slope � 10 and the line passes
through the point (2, 3) through the point (3, 5)
y � 3 � �5( x � 2)
y � 3 � �5x � 10
y � �5x � 13
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7. Slope � 7 and the line passes through 8. Slope � �3 and the line passes the
point (1, �4) through the point (5, �6)
Determine the slope-intercept form of the equation of the line passing through each pair of points.
9. (1, 2) and (5, 3) 10. (2, 6) and (5, 8)
m � 3 � 2 ______ 5 � 1
� 1 __ 4
y � 3 � 1 __ 4 ( x � 5)
y � 1 __ 4 x � 5 __
4 � 3
y � 1 __ 4 x � 7 __
4
11. (�2, 5) and (4, �3) 12. (1, �7) and (5, �3)
13. (0, 3) and (1, 3) 14. (2, 4) and (3, 4)
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Determine the slope-intercept form of the equation of each line, given the equation of a line parallel to the line and a point on the line.
15. y � 3x � 2, (1, 4) 16. y � 5x � 6, (3, 5)
4 � 3(1) � b
1 � b
y � 3x � 1
17. y � �2 x � 3, (�2, 6) 18. y � �4x � 1, (3, �4)
19. y � 1 __ 3 x � 11, (6, 5) 20. y � �3 __
2 x � 10, (4, �3)
Determine the slope-intercept form of the equation of each line, given the equation of a line perpendicular to the line and a point on the line.
21. y � 3x � 1, (2, 4) 22. y � 4x � 3, (1, 1)
m1 � � 1 ___ m2 � � 1 __
3
y � 4 � � 1 __ 3 ( x � 2)
y � � 1 __ 3 x � 2 __
3 � 4
y � � 1 __ 3 x � 14 ___
3
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23. y � 1 __ 3 x � 2, (3, �2) 24. y � �3 __
4 x � 9, (�5, 1)
25. y � �1 __ 5 x � 6, (0, 3) 26. y � 1 __
4 x � 2, (1, 0)
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Skills Practice Skills Practice for Lesson 1.7
Name _____________________________________________ Date ____________________
Absolutely! Absolute Value in Equations and Inequalities in One and Two Variables
Vocabulary Match each example with the term that describes it.
1. | x � 2| � 3 a. absolute value expression
2. |3x| b. absolute value equation
3. 2|3x � 1| � 2 � 5 c. absolute value inequality
4. 2 � 4x � 5 � 8 d. compound inequality
Problem Set Solve each equation.
1. |x � 3| � 4 2. |x � 2| � 5
x � 3 � �4
x � �3 � 4
x � �7, 1
3. |x � 1| � 2 � 7 4. |x � 3| � 4 � 10
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5. |2x � 3| � 8 6. |�x � 4| � 1
Graph each equation.
7. y � |x � 3| 8. y � |x � 2|
9. y � |3x � 6| 10. y � |4x � 16|
1
2
3
4
–1
–2
–3
–4
y
1 3 42–3–4 –2 –1 x
y = |x + 3|
0
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11. y � |�x � 3| 12. y � |2x � 8|
Solve each inequality and graph its solution on a number line.
13. |3x � 12| � 3 14. |4x � 22| � 2
3x � 12 � �3 or 3x � 12 � 3
3x � 9 or 3x � 15
x � 3 or x � 5
15. |�x � 3| � 5 16. |x � 10| 4
17. | 2 __ 3 x � 4 | � 2 18. | � 1 __
4 x � 2 | 1
6 8 9 107210 3 4 5
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Graph each inequality.
19. y � | x � 3| 20. y � | x � 1|
21. y |3x � 6| 22. y � |�x � 2|
23. y � |4x � 16| 24. y � |�3x � 12|
1
2
3
4
–1
–2
–3
–4
y
1 3 42–3–4 –2 –1 x
y > |x – 3|
0
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Skills Practice Skills Practice for Lesson 1.8
Name _____________________________________________ Date ____________________
Inverses and Pieces Functional Notation, Inverses, and Piecewise Functions
Vocabulary Give an example of each term.
1. relation
2. domain
3. range
4. function
5. inverse operations
6. functional notation
7. identity function
8. inverse functions
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9. composition of functions
10. piecewise function
Problem Set Rewrite each linear function using functional notation.
1. y � 2x � 3 2. y � �3x � 1
f( x) � 2 x � 3
3. 2x � 3y � 6 4. 3x � 2y � 12
Calculate the value of each function for the given values of the independent variable.
5. f( x) � 2x, calculate f(�1) and f(2)
f(�1) � �2; f(2) � 4
6. f( x) � �x, calculate f(�3) and f(4)
7. k( x) � �3x � 5, calculate k(�5) and k(8)
8. k( x) � 4x � 2, calculate k(0) and k(6)
9. g( x) � x2 � 2x, calculate g(�3) and g(2)
10. g( x) � �2x2 � 3, calculate g(�1) and g(4)
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Determine the inverse of each function.
11. f( x) � �4x 12. f( x) � 2x
f�1( x) � � 1 __ 4
x
13. g( x) � 5x � 2 14. g( x) � �3x � 4
15. h( x) � 2.3x � 1.3 16. h( x) � �4.5x � 5.6
For the functions f( x) � x � 2 and g( x) � �3x, calculate each composition.
17. f(g(2)) 18. g(f(2))
f(g(2)) � f(�6) � �6 � 2 � �4
19. g(f(�3)) 20. f(g(�3))
21. f(f(2)) 22. g(g(2))
Graph each piecewise function.
23. f( x) � � 2x � 1 x � 2 �x � 4 x � 2
24. f( x) � � �x � 4 x �1
2x � 1 x � �1
1
2
3
4
5
–1
–2
–3
y
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25. g( x) � � �x � 1 x � �1
2x �1 x 2 �x � 2 x � 2
26. g( x) � � x x �4 �2x � 3 �4 � x � 1 �x x � 1
Write a piecewise function to model each situation.
27. A rental car company charges $0.35 per mile for the first 200 miles. After 200 miles
they charge $0.20 per mile. Let c(m) be the cost for driving m miles.
c(m) � � 0.35m m � 200 0.2m m � 200
28. A laundromat charges $1.25 per pound of laundry for the first 10 pounds needed to
be cleaned. After 10 pounds they charge $0.75 per pound. Let c(l) be the cost for
cleaning l pounds of laundry.
29. A movie theatre charges $5.00 per ticket for people between the ages of 0 and
15 years. They charge $7.50 per ticket for people above the age of 15. Let c(a)
be the cost of a movie if a person’s age is a years.
30. A garage will inflate bicycle tires that are smaller than 20 inches in diameter for
$1.50. They charge $2.25 to inflate bicycle tires that are 20 inches or larger. Let
c(d ) be the cost to inflate a bicycle tire that has a diameter of d inches.
Chapter 1 l Skills Practice 333
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31. A home-and-garden store charges $10.25 for a cubic yard of gravel if you buy
10 cubic yards or less. They charge $9.50 for a cubic yard of gravel if you buy
between 10 and 15 cubic yards. They charge $8.75 for a cubic yard of gravel if you
buy 15 cubic yards or more. Let c( y) be the cost of y cubic yards of gravel.
32. An airline charges different ticket prices based on the number of miles a plane
travels. If a plane travels less than 500 miles, an airline will charge $0.85 per mile.
If a plane travels 500 miles to 1500 miles, they charge $0.70 per mile. If a plane
travels more than 1500 miles, they charge $0.55 per mile. Let c(m) be the cost to fly
m miles.
334 Chapter 1 l Skills Practice
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