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ALGEBRA 1UNIT 4
(9 LESSONS + 2 QUIZ + 2 PRACTICE+ 1 STUDY GUIDE + 1 TEST = 15 DAYS)
Date Lesson Plan Standard(s) Other
Th 11/30 4-N1 Put Equations into Slope-Intercept Form, F.IF.6, F.IF.7 Start Warm UpsDomain and Range
F 12/1 4-N2 Situational Equations, Appropriate Domain F.BF.1, F.IF.4, F.IF.5 Collect HW Set #11
M 12/4 4-N3 Verify Point as Solution, Function A.REI.10, Hand Out HW Set #12Notation A.REI.11, F.IF.2
T 12/5 4-N4 Determine Functions, One-to-One F.IF.1, F.IF.4 Warm Up QuizFunctions, Nature of the Graph, F.BF.3Intercepts/Intervals, Transformations
W 12/6 4-N5 Rate of Change Start Warm Ups
Th 12/7 PRACTICE
F 12/8 QUIZ Collect HW Set #12
M 12/11 4-N6 Solve Systems using Elimination A.REI.5 Warm Up Quiz & Hand Out HW Set
#13
T 12/12 PRACTICE Start Warm Ups
W 12/13 QUIZ
Th 12/14 4-N7 Systems of Equations Word Problems A.REI.5
F 12/15 4-N8 Systems of Equations Word Problems A.REI.5 Warm Up Quiz & Collect HW Set
#13
M 12/18 4-N9 Arithmetic Sequences F.IF.3
T 12/19 STUDY GUIDE
W 12/20 TEST
4 - N1Today, you will be able to:
Graph the following lines:
1. y+x=3 2. 2 x+ y=1 3. x+3 y=6
Remember, the SLOPE of a line is the same as the
______________________________________!
4. Which graph would have a steeper slope?
y=5 x−9 OR y=3 x+6
5. Which graph would have a steeper slope?
8 y=2 x+16 OR 2 y−x=8
Remember, DOMAIN is the _____________________ and
RANGE is the ______________________!
6. What is the domain of the relation shown below?
{( 4,2 ) , (1,1 ) , (0,0 ) , (1 ,−1 ) , (4 ,−2 ) }
(1) {0,1,4 } (3) {−2 ,−1,0,1,2,4 }
(2) {−2 ,−1,0,1,2 } (4) {−2 ,−1,0,0,1,1,1,2,4,4 }
7. What is the range of the relation shown below?
{( 4,2 ) , (1,1 ) , (0,0 ) , (1 ,−1 ) , (4 ,−2 ) }
(1) {0,1,4 } (3) {−2 ,−1,0,1,2,4 }
(2) {−2 ,−1,0,1,2 } (4) {−2 ,−1,0,0,1,1,1,2,4,4 }
8. Let f be a function such that f ( x )=3 x−1 is defined on the domain [ 2,8 ] . What is the range of this function?
9. Let f be a function such that f ( x )=3
4x+2
is defined on the domain [ 0 , 12 ] . What is the range of this function?
10. Officials in a town use a function, C, to analyze traffic patterns. C(n) represents the rate of traffic through an intersection where n is the number of observed vehicles in a specified time interval. What would be the most appropriate domain for the function?
(1) {…-2, -1, 0, 1, 2, 3, …} (3) {0, 0.5, 1, 1.5, 2, 2.5}
(2) {-2, -1, 0, 1, 2, 3} (4) {0, 1, 2, 3, …}
11. Which domain would be the most appropriate set to use for a function that predicts the number of household online-devices in terms of the number of people in the household?
(1) integers (3) irrational numbers
(2) whole numbers (4) rational numbers
12. A store sells self-serve frozen yogurt sundaes. The function C(w) represents the cost, in dollars, of a sundae weighing w ounces. An appropriate domain for this function would be
(1) integers (3) nonnegative integers
(2) rational numbers (4) nonnegative rational numbers
4 – N2Today, you will be able to:
1. Amanda babysits for her cousin. Her earnings can be modeled by the equation e ( x )=5 x , where x represents the number of hours Amanda babysits. What does the value 5 represent in this scenario?
2. Stanley wants to go to the carnival. The cost of attending the carnival can be modeled by the equation c ( x )=9+1. 75 x , where x represents the number of rides Stanley goes on.
What could the value 9 represent in this scenario?
What does the value 1.75 represent?
3. A plumber has a set fee for a house call and charges by the hour for repairs. The total cost of her services can be modeled by the function c ( t )=125 t+95 .
Which statements about this function are true?I. A house call fee costs $95.II. The plumber charges $125 per hour.III. The number of hours the job takes is represented by t.
(1) I and II, only (3) II and III, only
(2) I and III, only (4) I, II, and III4. The owner of a small computer repair business has one employee who is paid
an hourly rate of $22. The owner estimates his weekly profit using the function P( x )=8600−22 x . In this function, x represents the number of
(1) computers repaired per week
(2) hours worked per week
(3) customers served per week
(4) days worked per week
5. A company that manufactures radios first pays a start-up cost, and then spends a certain amount of money to manufacture each radio. If the cost of manufacturing r radios is given by the function c (r )=5 .25 r+125 , then the value 5.25 best represents
(1) the start-up cost
(2) the profit earned from the sale of one radio
(3) the amount spent to manufacture each radio
(4) the average number of radios manufactured
6. Alex makes ceramic bowls to sell at a monthly craft fair in a nearby city. Every month, she spends $50 on materials for the bowls from a local art store. At the fair, she sells each completed bowl for a total of $25 including tax. Which equation expresses Alex’s profit as a function of the number of bowls that she sells in one month?
(1) p( x )=50 x+25 (3) p( x )=25 x
(2) p( x )=15 x+25 (4) p( x )=25 x−50
7. The cost of belonging to a gym can be modeled by C (m )=50 m+79 .50 , where C(m) is the total cost for m months of membership.
State the meaning of the slope and y-intercept of this function with respect to the costs associated with the gym membership.
8. Caitlin has a movie rental card worth $175. After she rents the first movie, the card’s value is $172.25. After she rents the second movie, its value is $169.50. After she rents the third movie, the card is worth $166.75.
Assuming the pattern continues, write an equation to define A(n), the amount of money on the rental card after n rentals.
Caitlin rents a movie every Friday night. How many weeks in a row can she afford to rent a movie, using her rental card only? Explain how you arrived at your answer.
4 – N3Today, you will be able to:
1. Is the point (−2 ,−1 ) a solution of y=2 x+3?
VERIFYING A POINT AS A SOLUTION ALGEBRAICALLY:
Is the point (−2 ,−1 ) on the line y=2 x+3 ?
2. Does the line pass through the point ?
3. Does the point lie on the line ?
4. Sue and Kathy were doing their algebra homework. They were asked to write
the equation of the line that passes through the points (−3,4 ) and (6,1 ) . Sue
wrote y−4=−1
3( x+3 )
and Kathy wrote y=−1
3x+3
. Justify why both students are correct.
EVALUATING A FUNCTION:
5. If f ( x )=x+3 , evaluate f (5 ) .
6. If f ( x ) =- 3
4x+10
, evaluate f (−8 ) .
7. If f ( x )=2
3x−1
, evaluate f ( 3
2 ).
8. If f ( x )=√2x+3
6 x−5 , evaluate f ( 1
2 ).
9. If f ( n )=(n−1 )2+3 n , which statement is true?
(1) f (3 )=−2
(2) f (−2 )=3
(3) f (−2 )=−15
(4) f (−15 )=−2
10. Consider the relation f below.
f = {(10 ,5 ) , (12 ,6 ) , (14 ,6 ) , (16 ,7 ) }
a) What is f (16 ) ?
b) If f ( x )=6 , then what might x be?
4 – N4Today, you will be able to:
1. Graph the following relation:y =- 1
2x+1
Is this relation a function?
Is this relation a one-to-one function?
Nature of the Graph:
x-intercept:
y-intercept:
DETERMINING FUNCTIONS ALGEBRAICALLY:
2. Which set of ordered pairs represents a function?
(1) {(0,4 ) , (2,4 ) , (2,5 ) } (3) {( 4,1 ) , (6,2 ) , (6,3 ) , (5,0 ) }
(2) {(6,0 ) , (5,0 ) , (4,0 ) } (4) {(0,4 ) , (1,4 ) , ( 0,5 ) , (1,5 ) }3. Which table represents a function?
4. The function f has a domain of {1 , 3 , 5 , 7 } and a range of {2 , 4 , 6 } .
Could f be represented by {(1,2 ) , (3,4 ) , (5,6 ) , (7,2 ) }?Justify your answer.
DETERMINING ONE-TO-ONE FUNCTIONS ALGEBRAICALLY:
5. Is the relation {(6,0 ) , (5,0 ) , (4,0 ) } one-to-one?
6. Is the relation {( 2 , 1 ) , ( 4 , 4 ) , (6 , 5 ) } one-to-one?
DETERMING THE NATURE OF THE GRAPH ALGEBRAICALLY:
7. What is the nature of the graph y=3 x−7 ?
8. What is the nature of the graph f ( x ) =- 3
2x
?
DETERMINING THE X-INTERCEPT ALGEBRAICALY:
DETERMINING THE Y-INTERCEPT ALGEBRAICALY:
9. 3 x+2 y=12
What is the x-intercept? What is the y-intercept?
10. 7 x−4 y=56
What is the x-intercept? What is the y-intercept?
The graphs of all functions in the FAMILY OF LINEAR FUNCTIONS
are __________________________.
Each family of functions has a __________________________________, the most basic function in the family.
The family of linear functions has the parent function _________________.
A change to the equation of a function causes a change to the graph.
This change to the graph is called a _______________________________.
VERTICAL TRANSLATION:
If you ADD a constant, shift the parent function _________.
If you SUBTRACT a constant, shift the parent function ___________.
11. If you were to graph the function y =- 3
2x−1
, and then you performed a vertical translation 7 units up, what would be the equation of this new function?
12. If you were to graph the function y =- x+4 , and then you performed a vertical translation 10 units down, what would be the equation of this new function?
4 – N5Today, you will be able to:
REMEMBER, The formula for AVERAGE RATE OF CHANGE is:
1. What is the rate of change between the points (1 , 7 ) and (3 , 15 ) ?
2. What is the rate of change between the points (2 , 8 ) and (17 , 3 )?
3. What is the rate of change between the points (6 , 10 ) and (−2 , 11) ?
4. Joey enlarged a 3-inch by 5-inch photograph on a copy machine. He enlarged it four times. The table below shows the area of the photograph after each enlargement.
What is the average rate of change of the area from the original photograph to the fourth enlargement, to the nearest tenth?
5. The table below shows the average diameter of a pupil in a person’s eye as he or she grows older.
What is the average rate of change, in millimeters per year, of a person’s pupil diameter from age 20 to age 50?
6. The table below shows the year and the number of households in a building that had high-speed broadband internet access.
Year 2002 2003 2004 2005 2006 2007
Number of Households
11 16 23 33 42 47
For which interval of time was the average rate of change the smallest?
(1) 2002 - 2004
(2) 2003 - 2005
(3) 2004 - 2006
(4) 2005 - 2007
7. Which function has a constant rate of change equal to -3?
8. Which representations are functions?
9. A function is shown in the table below.
Which ordered pair, (−4 , 1 ) or (1 , −4 ) , would result in a relation that is no longer a function? Explain your answer.
10. A mapping is shown in the diagram below.
This mapping is
(1) a function, because Feb has two outputs, 28 and 29
(2) a function, because two inputs, Jan and Mar, result in the output 31
(3) not a function, because Feb has two outputs, 28 and 29
(4) not a function, because two inputs, Jan and Mar, result in the output 31
4 – N6Today, you will be able to:
1. Solve the system of equations graphically:
y+x=4y−x=2
Systems of equations can also be solved algebraically. The method used today is called the ELIMINATION METHOD.
To solve a linear system by elimination, you need two things:
_________________________ and ___________________________
y+x=4y−x=2
2.
x+8 y=114 x−8 y=4
3.
4 x+3 y=72 x−3 y=8
4.
6 x+2 y=23 x−3 y=9
5.
3 x+5 y =-8x−2 y=1
6.
3 x+2 y=85 x+2 y=12
7. Which system of equations does not have the same solution as the system below?
4 – N7Today, you will be able to:
1. Alexandra purchased two doughnuts and three cookies at a bakery and is charged $3.30. Brianna purchased five doughnuts and two cookies at the same shop for $4.95.
Write a system of equations to find the price of one doughnut and the price of one cookie.
Using these equations, determine and state the price of a doughnut and the price of a cookie, to the nearest cent.
2. Jacob and Zachary go to the movie theater and purchase refreshments for their friends. Jacob spends a total of $18.25 on two bags of popcorn and three drinks. Zachary spends a total of $27.50 on four bags of popcorn and two drinks.
Write a system of equations that can be used to find the price of one bag of popcorn and one drink.
Using the equations, determine and state the price of a bag of popcorn and the price of a drink, to the nearest cent.
3. For a class picnic, two teachers went to the same store to purchase drinks. One teacher purchased 18 juice boxes and 32 bottles of water and spent $19.92. The other teacher purchased 14 juice boxes and 26 bottles of water, and spent $15.76.
Write a system of equations to represent the costs of a juice box, j, and a bottle of water, w.
Kara said that the juice boxes might have cost 52 cents each and that the bottles of water might have cost 33 cents each. Use your system of equations to justify that Kara’s prices are not possible.
Solve your system of equations to determine the actual cost, in dollars, of each juice box and each bottle of water.
4 – N8Today, you will be able to:
1. The Celluloid Cinema sold 150 tickets to a movie. Some of these were child tickets and the rest were adult tickets. A child ticket cost $7.75 and an adult ticket cost $10.25. If the cinema sold $1470 worth of tickets, which system of equations could be used to determine how many adult tickets, a, and how many child tickets, c, were sold?
(1)
a+c=147010 .25 a+7 .75 c=150 (3)
a+c=15010 .25 a+7 .75 c=1470
(2)
a+c=1507 .75 a+10 .25 c=1470 (4)
a+c=14707 . 75 a+10 .25 c=150
2. Last week, a candle store received $355.60 for selling 20 candles. Small candles sell for $10.98 and large candles sell for $27.98. How many large candles did the store sell?
3. A dry cleaning service charges $1.25 per shirt to be dry-cleaned and $3.50 per pair of pants to be dry-cleaned. Lydia noticed that the dry cleaning business collected $64.50 dry-cleaning shirts and pants on Friday.
Write an equation to represent the possible number of shirts and pants that could have been dry-cleaned on Friday.
Lydia said that there might have been 13 shirts and 17 pairs of pants that were dry-cleaned on Friday. Are Lydia’s numbers possible? Use your equation to justify your answer.
Later, Lydia found a record showing that there were a total of 30 shirts and pants that were dry-cleaned on Friday. How many shirts were dry-cleaned on Friday?
4. Franco and Caryl went to a bakery to buy desserts. Franco bought 3 packages of cupcakes and 2 packages of brownies for $19. Caryl bought 2 packages of cupcakes and 4 packages of brownies for $24. Let x equal the price of one package of cupcakes and y equal the price of one package of brownies.
Write a system of equations that describes the given situation.
Determine the exact cost of one package of cupcakes and the exact cost of one package of brownies in dollars and cents. Justify your solution.
4 – N9Today, you will be able to:
SEQUENCE:
ELEMENT:
ARITHMETIC SEQUENCE:
COMMON DIFFERENCE:
1. Find the common difference in the arithmetic sequence:
3, 5, 7, 9, …
2. Find the common difference in the arithmetic sequence:6, 14, 22, 30, …
3. Find the common difference in the arithmetic sequence:-3, 2, 7, 12, 17, …
4. Find the common difference in the arithmetic sequence:14, 8, 2, -4, …
5. Find the common difference in the arithmetic sequence:25, 22, 19, 16, …
6. Find the next three terms in the arithmetic sequence:4, 17, 30, 43, …
7. Find the next three terms in the arithmetic sequence:3, 7, 11, 15, …
8. Find the next three terms in the arithmetic sequence:16, 7, -2, -11, …
9. Find the next three terms in the arithmetic sequence:-13, -11, -9, -7, …
To find the nth term of an arithmetic sequence, use the formula:
an=a1+( n−1 ) dwhere a1 is
d is
** This formula is given to you on the reference sheet!
10. In a sequence, the first term is 4 and the common difference is 3. What is the fifth term of this sequence?
11. In a sequence, the first term is 8 and the common difference is 7. What is the forty-second term of this sequence?
12. Find the 12th term of the arithmetic sequence 3, 8, 13, 18, …
13. Find the 20th term of the arithmetic sequence 5, 9, 13, 17, 21, ….
14. Find the 8th term of the arithmetic sequence 10, 3, -4, -11, -18, …
15. Find the 15th term of the arithmetic sequence 11, 15, 19, 23, …
16. Find the 11th term of the arithmetic sequence 100, 88, 76, 64, …
17. Find the 30th term of the arithmetic sequence 1.2, 1.8, 2.4, 3, …
UNIT 4 – STUDY GUIDE
4-N11. Graph the line:
3 x+ y=1
4-N22. If the function f(x) represents the number of words that Janet can type in x
minutes, what is the possible domain for the function?
(1) the set of integers (3) the set of non-negative integers
(2) the set of real numbers (4) the set of irrational numbers
3. Andy has been working as a deliveryman. He earns a $50 flat rate per day, plus an additional $5 for each delivery he makes. Write his earnings, e(x), as a function of the number of deliveries that he made.
4-N3
4. Does the point (2 ,−4 ) lie on the line whose equation is y =-3 x+2 ?
5. If f ( x ) =- 2
3x−7
, evaluate f ( 9 ) .
4-N46. Which of the following is not a function?
(1) {(2,7 ) , (5,8 ) , (3,9 ) } (3) {(−2,6 ) , (3 , 10 ) , (−2,2 ) }
(2) {(2,6 ) , (3,6 ) , (4,6 ) } (4) {(−2 ,−2 ) , (3,3 ) , (−5 ,−5 ) }
7. Which of the following is a one-to-one function?
(1) {(2,7 ) , (5,8 ) , (3,7 ) } (3) {(−2,6 ) , (3 , 10 ) , (−2,2 ) }
(2) {(2,6 ) , (3,6 ) , (4,6 ) } (4) {(−2 ,−2 ) , (3,3 ) , (−5 ,−5 ) }
8. What is the x-intercept of the line whose equation is 2 x+3 y=6?
4-N59. The table below shows the year and the number of households in a building
that had high-speed broadband internet access.
Year 2002 2003 2004 2005 2006 2007Number of Households
11 16 23 33 42 47
What was the average rate of change between 2002 and 2007?
4-N6
10. Which pair of equations could not be used to solve the following equations for x and y?
4 x+2 y=22−2 x+2 y=−8
(1)
4 x+2 y=222 x−2 y=8 (3)
12 x+6 y=666 x−6 y=24
(2)
4 x+2 y=22−4 x+4 y=−16 (4)
8 x+4 y=44−8 x+8 y=−8
4-N7/4-N8
11. Mo’s farm stand sold a total of 165 pounds of apples and peaches. She sold apples for $1.75 per pound and peaches for $2.50 per pound. If she made $337.50, how many pounds of peaches did she sell?
(1) 11
(2) 18
(3) 65
(4) 100
12. Leah and Melissa go to the bookstore and purchase snacks for their friends. Leah spends a total of $7.25 on three drinks and seven bags of chips. Melissa spends a total of $5.50 on two drinks and six bags of chips.
Write a system of equations that can be used to find the price of one drink and one bag of chips.
Determine and state the price of a drink and a bag of chips.
4-N9
13. Find the 23rd term of the arithmetic sequence 4, 15, 26, 37, …
