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ALGEBRA 1
UNIT 10
(1 SMART LIVING FAIR + 7 LESSONS + 1 QUIZ + 1 PRACTICE + 1 STUDY GUIDE + 1 TEST = 12 DAYS)
Date Lesson Plan Standard(s) Other
Th 4/18 SMART LIVING FAIR
M 4/29 10-N1 Distinguish between Linear (Arithmetic) F.LE.1 COMMON CORE WARM UP And Exponential (Geometric) & Hand Out HW Set #29
T 4/30 10-N2 Recursive Formulas F.LE.1 COMMON CORE WARM UP
W 5/1 10-N3 Explicit Formulas F.LE.1 COMMON CORE WARM UP
Th 5/2 10-N4 Combine Recursive & Explicit Formulas F.LE.1 COMMON CORE WARM UP
F 5/3 PRACTICE Warm Up Quiz& Collect HW Set #29
M 5/6 QUIZ COMMON CORE WARM UP& Hand Out HW Set #30
T 5/7 10-N5 Square Root Functions F.IF.7 COMMON CORE WARM UP
W 5/8 10-N6 Absolute Value Graph & Transformations F.IF.7 COMMON CORE WARM UP
Th 5/9 10-N7 Graph Piece-Wise Functions F.IF.7 COMMON CORE WARM UP
F 5/10 STAFF DEVELOPMENT DAY
M 5/13 STUDY GUIDE Warm Up Quiz& Collect HW Set #30
T 5/14 TEST
10 – N1Today, you will be able to:
“TOP FIFTEEN” TOPIC1. What kind of equation is y=5 x−4 ?
This is a portion of the x/y chart for y=5 x−4 .
x y
2 6
3 11
4 16
5 21
6 26
Find the average rate of change between each set of points.
What do you notice about the average rate of change for a linear equation?
In a linear equation, average rate of change will always be ______________.
In a linear equation, average rate of change is the same as _____________.
The y-values of a linear equation form an ___________________________!
2. What kind of equation is ?
This is a portion of the x/y chart for .
x y0 2
1 5
2 113 234 47
Find the average rate of change between each set of points.
What do you notice about the average rate of change for an exponential equation?
In an exponential equation, average rate of change will always have a
___________________________.
The rates of change of an exponential equation form a
___________________________!
3. Caleb claims that the ordered pairs shown in the table below are from a nonlinear function.
State whether Caleb is correct. Explain your reasoning.
4. The function, t(x), is shown in the table below.
Determine whether t(x) is linear or exponential. Explain your answer.
5. Consider the pattern of squares shown below:
Which type of model, linear or exponential, should be used to determine how many squares are in the nth pattern? Explain your answer.
6. Rachel and Marc were given the information shown below about the bacteria growing in a Petri dish in their biology class.
Rachel wants to model this information with a linear function. Marc wants to use an exponential function. Which model is the better choice? Explain why you chose this model.
LINEAR EQUATIONS have a _________________ rate of change.
This means they will ____________ or _____________ by a constant amount!!
They have an EQUAL DIFFERENCE OVER AN EQUAL INTERVAL!
EXPONENTIAL EQUATIONS have a rate of change with a _____________.
Look for words like percent (%), double, triple, one-half, one-third, multiplied by, etc.
7. The highest possible grade for a book report is 100. The teacher deducts 10 points each day the report is late.
Which kind of function describes this situation?
(1) linear (3) exponential growth
(2) quadratic (4) exponential decay
8. Which situation could be modeled using a linear function?
(1) a bank account balance that grows at a rate of 5% per year, compounded annually
(2) a population of bacteria that doubles every 4.5 hours
(3) the cost of a cell phone service that charges a base amount plus 20 cents per minute
(4) the concentration of medicine in a person’s body that decays by a factor of one-third every hour
9. Which scenario represents exponential growth?
(1) A water tank is filled at a rate of 2 gallons/minute.
(2) A vine grows 6 inches every week.
(3) A species of fly doubles its population every month during the summer.
(4) A car increases its distance from a garage as it travels at a constant speed of 25 miles per hour.
10. Grisham is considering the three situations below.I. For the first 28 days, a sunflower grows at a rate of 3.5 cm per day.II. The value of a car depreciates at a rate of 15% per year after it is
purchased.III. The amount of bacteria in a culture triples every two days during
an experiment.
Which of the statements describes a situation with an equal difference over an equal interval?
(1) I, only (3) I and III
(2) II, only (4) II and III
10 – N2Today, you will be able to:
RECURSIVE FORMULA:
f ( n ) represents ___________________________.
f ( n+1 ) represents ____________________________.
f ( n−1 ) represents ______________________________.
You can also see f ( n ) written as _____________.
You can also see f ( n+1 ) written as _____________.
You can also see f ( n−1 ) written as _____________.
HINT:
1. If a function is defined recursively by f (1 )=5 and f ( n+1 )=f ( n )−2 ,
then evaluatef (2 ) .
2. If a function is defined recursively by f (1 )=−4 and f ( n+1 )=3 f (n ) , then evaluatef (2 ) .
3. If a function is defined recursively by f (0 )=2 and f ( x+1 )=f ( x )+8 , then evaluate f (3 ) .
4. If a function is defined recursively by f (1 )=2 and f ( n+1 )=5 f (n )−4 , then evaluate f (3 ) .
5. Find the f (5 ) in the sequence which is recursively defined as f (1 )=7 and f ( n )=3 f (n−1 )−1 .
6. Find a3 of the sequence which is recursively defined as a1=- 2 and an= (−3 ) an−1+4 .
7. Find a5 of the sequence which is recursively defined as a1=19 and an=an−1−2 .
8. Write the first five terms of the recursive sequence defined below.
9. If and , what is the value of ?
(1) 5 (3) 120
(2) 20 (4) 72010. Which recursively defined function represents the sequence
3, 7, 15, 31, …?
(1)
(2)
(3)
(4)
11. Which function could be used to represent the sequence 8, 20, 50,
125, 312.5,…, given that ?
(1) (3)
(2) (4)
10 – N3Today, you will be able to:
EXPLICIT FORMULA:
*** Formula for Arithmetic Sequence: an=a1+( n−1 ) d
1. Write the explicit formula for the sequence: 25, 35, 45, 55, …
Use the explicit formula to find the 12th term.
2. Write the explicit formula for the sequence: 14, 10, 6, 2, …
Use the explicit formula to find the 13th term.
3. Write the explicit formula for the sequence 8, 5, 2, -1, …
4. The diagrams below represent the first three terms of a sequence.
Assuming the pattern continues, which formula determines an , the number of shaded squares in the nth term?
(1) an=4 n+12 (3) an=4n+4
(2) an=4n+8 (4) an=4 n+2
5. Andy has $310 in his account. Each week, w, he withdraws $30 for his expenses. Which expression could be used if he wanted to find out how much money he had left after 8 weeks?
(1) (3)
(2) (4)
6. In 2013, the United States Postal Service charged $0.46 to mail a letter weighing up to 1 oz. and $0.20 per ounce for each additional ounce. Which function would determine the cost, in dollars, c(z), of mailing a letter weighing z oz. where z is an integer greater than 1?
(1)
(2)
(3)
(4)
7. Ashley programmed a website’s checkout process with an equation to calculate the amount customers will be charged when they download e-books.
The website offers a discount. If one e-book is bought at the full price of $9.99, then each additional e-book is $5.99.
State an equation that represents the cost, C, when e e-books are downloaded.
Ashley figured she would be charged $35.94 for 6 e-books. Is this the correct amount? Justify your answer.
10 – N4Today, you will be able to:
1. The third term in an arithmetic sequence is 10 and the fifth term is 26.
If the first term is a1 , which is an equation for the nth term of this sequence?
(1) an=8 n+10 (3) an=16 n+10
(2) an=8n−14 (4) an=16 n−38
2. Which recursively defined function has a first term equal to 10 and a common difference of 4?
3. For the sequence -27, -12, 3, 18, …, the expression that defines the
nth term where is
(1) (3)
(2) (4)
4. A pattern of blocks is shown below.
If the pattern of blocks continues, which formula(s) could be used to determine the number of blocks in the nth term?
(1) I and II (3) II and III
(2) I and III (4) III, only
5. In 2014, the cost to mail a letter was 49 cents for up to one ounce. Every additional ounce cost 21 cents. Which recursive function could be used to determine the cost of a 3-ounce letter, in cents?
(1)
(2)
(3)
(4)
6. A sequence of blocks is shown in the diagram below.
This sequence can be defined by the recursive function and
. Assuming the pattern continues, how many blocks will there by when ?
(1) 13 (3) 28
(2) 21 (4) 36
7. A sunflower is 3 inches tall at week 0 and grows 2 inches each week. Which function(s) shown below can be used to determine the height, f(n), of the sunflower in n weeks?
I. f (n)=2 n+3
II. f (n)=2 n+3 (n−1 )
III. f (n)=f ( n−1 )+2 where f (0)=3
(1) I and II (3) III, only
(2) II, only (4) I and III
8. Each day, Toni records the height of a plant for her science lab. Her data are shown in the table below.
The plant continues to grow at a constant daily rate. Write an equation to represent h(n), the height of the plan on the nth day.
9. Jackson is starting an exercise program. The first day he will spend 30 minutes on a treadmill. He will increase his time on the treadmill by 2 minutes each day. Write an equation for T(d), the time, in minutes, on the treadmill on day d.
Find T(6), the minutes he will spend on the treadmill on day 6.
UNIT 10 – PRACTICE #1
Answer the following multiple choice question.
1. Which equation models the data in the accompanying table?
(1) y=2 x+5 (2) y=5 (2x ) (3) y=2 x (4) y=2 x2
Answer the following question.
2. The function, f(x), is shown in the table below.
Determine whether f(x) is linear or exponential. Explain your answer.
Answer the following multiple choice questions.
3. The table below shows the average yearly balance in a savings account where interest is compounded annually. No money is deposited or withdrawn after the initial amount is deposited.
Which type of function best models the given data?
(1) linear function with a negative rate of change
(2) linear function with a positive rate of change
(3) exponential decay function
(4) exponential growth function
4. Lily wants to save money to buy a car. She is going to save $100 per month. What kind of function describes this situation?
(1) linear (3) exponential growth
(2) quadratic (4) exponential decay
5. Mr. Young got a new car. His car depreciates (loses value) by 12% each year. What kind of function describes this situation?
(1) linear (3) exponential growth
(2) quadratic (4) exponential decayAnswer the following question.
6. Determine and state whether the sequence 1, 5, 25, 125, … displays exponential behavior. Explain how you arrived at your decision.
Answer the following questions.
7. The explicit formula an=5 n−21 is used to generate a sequence of numbers. Find the 19th term of the sequence.
8. The recursive formula for a geometric sequence is
f (1 )=12
f ( x )=(23 ) f ( x−1 )
What is the next number in this sequence?
Answer the following multiple choice questions.
9. An arithmetic sequence is given: -12, -8, -4, 0, …
Identify the recursive formula for this sequence.
(1)
a1=- 12an=an−1−4 (3)
a1=- 12an=an−1+4
(2)
a1=- 12
an=an−1+(14 )(4)
a1=4an=an−1−12
10. If a sequence is defined recursively by f (0)=2 and f (n+1)=−2 f (n )+3 for n≥0 , then f (2) is equal to
(1) 1 (3) 5
(2) -11 (4) 17
11. The recursive formula for a sequence of numbers is:
a1=- 9an=an−1−8
Which equation would produce the same sequence of numbers?
(1) f ( n )=- 9 n
(2) f ( n )=n−8
(3) f ( n )=- n−8
(4) f ( n )=−8n−112. The recursive formula for an arithmetic sequence is:
f (1)=65f ( n )= f ( n−1 )−15
Which statement accurately describes this sequence?
(1) The sequence is 65, 50, 30, …
(2) The sequence is 65, -975, 14625, …
(3) The sixth term is negative.
(4) The second term is 80.
Answer the following.
13. Given the sequence 8, 11, 14, 17, …
Write an explicit formula for this sequence.
What is the 30th term in the sequence?
14. Andy is training for a chicken wing eating contest. The first day he will eat a total of 50 chicken wings. He will increase the number of chicken wings he eats by 15 each day. Write an equation for C(d), the number of chicken wings eaten on day d.
Find C(18), the number of chicken wings he will eat on day 18.
10 – N5Today, you will be able to:
1. Which graph represents ?
2. Draw the graph of on the set of axes below.
3. The graph of the function is shown below.
The domain of the function is
(1) (3)
(2) (4)
4. Draw the graph of on the set of axes below.
5. Graph the function on the set of axes below.
6. Which relation does not represent a function?
7. Graph over the domain .
10 – N6
Today, you will be able to:
ABSOLUTE VALUE:
The symbol used for absolute value:
WHERE IS ABSOLUTE VALUE ON CALCULATOR?
An absolute value function has a ____-shaped graph.
It is formed by two rays with a common endpoint, called the ____________.
As in a parabola, the vertex is either a _____________ or a _____________.
The branches of the function are ______________________.
1. Graph y=|x|
2. Graph y=−|3 x|+2
3. What is the minimum value of the function ?
(1) -2 (3) 3
(2) 2 (4) -3
4. The function h(x), which is graphed below, and the function
are given.
Which statements about these functions are true?
I. g(x) has a lower minimum value than h(x).
II. For all values of x, .
III. For any value of x, .
(1) I and II, only (3) II and III, only
(2) I and III, only (4) I, II, and III
5. Graph the function y=|x−3| on the set of axes below.
Explain how the graph of y=|x−3| has changed from the related
graph y=|x|.
6. On the set of axes below, graph f ( x )=|2 x|.
If g( x )=f ( x )+4 , how is the graph of f(x) translated to form the graph of g(x)?
If h( x )=f (x+7 ) , how is the graph of f(x) translated to form the graph of h(x)?
7. Given the parent function , the function
is the result of a shift of f(x)
(1) 1 unit left and 2 units down
(2) 1 unit left and 2 units up
(3) 1 unit right and 2 units down
(4) 1 unit right and 2 units up
10 – N7
Today, you will be able to:
PIECEWISE FUNCTION:
1. Which graph represents f ( x )=¿ {|x| x<1 ¿¿¿¿
?
2. Graph
3. Graph
4. Graph
How many values of x satisfy the equation ? Explain your answer, using evidence from your graphs.
UNIT 10 – STUDY GUIDE
1. Given the following table:
x -1 0 1 2
y 5 1 -3 -7
Is this a linear or exponential function? Explain your answer.
2. Thomas bought a new car ten years ago. Each year, the car has gone down in value by 8%. Which statement correctly describes the graph that represents this situation?
(1) The graph would decrease by a constant factor of 1.08.
(2) The graph would be a linear function with a slope of -8.
(3) The graph would be exponential and decrease over time.
(4) The graph would be exponential and increase over time.
3. Which table of values represents f ( x )=2 x−1 ?
4. The recursive formula for a sequence of numbers is:a1=8an=an−1−6
Find a3 .
*** Formula for Arithmetic Sequence:an=a1+( n−1 ) d
5. Given the sequence of numbers 3, 13, 23, 33, 43, …
Write the explicit formula for this sequence.
6. The recursive formula for a sequence of numbers is:
a1=4an=an−1+12
What is the explicit formula that would represent this sequence?
7. Which equation is represented in the accompanying graph?
(1) y=|x|−3 (3) y=|x+3|−1
(2) y= (x−3 )2+1 (4) y=|x−3|+1
8. On the set of axes below, graph f ( x )=|3 x|.
If g( x )=f ( x )+3 , how is the graph of f(x) translated to form the graph of g(x)?
If h( x )=f (x+6 ) , how is the graph of f(x) translated to form the graph of h(x)?
If j ( x )=−f ( x ), how is the graph of f(x) transformed to form the graph of j(x)?
9. Graph the following piecewise function:
10. Four relations are shown below.
State which relation(s) are functions.
Explain why the other relation(s) are not functions.
