Homework Unit 2 Day 1
Name: ________________________________
1. Fiona has an uncle named Joe. His heights were also marked on the door, and are shown in
the graph below.
What are the missing values in the data table? (Don’t forget units)
Age 2, Height ______
Age 4, Height ______
Age 5, Height ______
Age 7, Height ______
Age 8, Height ______
Age 11, Height _____
Age 14, Height _____
Age 17, Height _____
Age 18, Height _____
2. Evaluate the following:
a. −3 + (−7)
3. Evaluate:
2𝑥 + 7 when 𝑥 = −2
b. −12 + 16
c. (−9) + (−4)
4. Sammy is retiling the floor in his living
room. If his floor is 12 feet by 14 feet, and
each tile is 1𝑓𝑡 2 , how many tiles will he
need to buy?
5. Write the verbal sentence as an equation,
expression, or an inequality.
Four more than a number is less than twice a
number minus seven.
6. Check the solution to the following:
4𝑥 − 7 = 5; 𝑥 = 4
7. Which of the following is not a function:
a)
x
0
1
2
1
y
1
2
3
2
8. Convert:
19𝑐𝑚 to 𝑖𝑛𝑐ℎ𝑒𝑠
9. Convert:
88𝑓𝑡/𝑠𝑒𝑐 to 𝑚𝑝ℎ
b)
x
0
1
2
3
y
1
1
2
3
c)
x
0
1
2
1
y
1
2
3
4
Homework Unit 2 Day 2
Name: ________________________________
Use the graph and data table below to answer the following questions:
1. What does ℎ(5) mean?
2. Using the table and graph above, what is the
value of ℎ(4)?
3. Using the table and graph, estimate the value 4. Using the table and graph, find ℎ(7)?
of ℎ(0.5). Explain in words what ℎ(0.5)
Explain your answer.
means.
5. Find f(3), using the equation:
f(x) = 2x – 14
6. Find g(–3), using the equation:
g(x) = x2 + 2
7. Find the unit rate:
91 𝑚𝑖𝑙𝑒𝑠
13 ℎ𝑜𝑢𝑟𝑠
8. Which of the following is not a function:
9. Check the solution:
5(3 − 𝑥) < 5;
a)
x
0
1
2
1
𝑥=3
y
12
13
14
15
b)
x
0
1
2
3
y
18
15
10
10
c)
x
0
1
2
1
y
35
38
41
38
10. Evaluate:
a. −7 + (−4)
b. 9 + (−17)
c. −5 + 10
11. Simplify the expression:
9[5 + (−3)]
12. Is 𝑥 = 14 a solution to the equation:
3𝑥 + 2 = 45
13. A cheetah ran 300 feet in 2.92 seconds. What was the cheetah’s average speed in miles per
hour?(just set it up)
Homework Unit 2 Day 3
Name: ________________________________
1. Evaluate:
a. −3 + 9
2. Combine like terms:
4𝑥 + 7 − 9 + 12𝑥
b. 12 + (−7)
3. Write and equation, inequality, or expression
to model the real-life situation.
Ben’s hourly wage 𝑏 at his after school job is
$1.50 less than Eileen’s hourly wage 𝑒.
4. Evaluate the expression:
32 − 5 ∙ (2 + 1) + 4
Use the Graph Below to answer the following
questions:
5. What is the dependent and independent
variable?
1
6. At what age did Joe wear a 2 2?
7. If 𝑓(𝑥) is Joe’s shoe size at 𝑥 years of age,
what is 𝑓(6)?
8. What is 𝑥 if 𝑓(𝑥) = 4.5?
9. What information does the graph give you?
10. What would you expect 𝑓(7) to be?
Explain why.
Homework Unit 2 Day 4
Name: ________________________________
Ray runs an A/C business called Air4All. He charges a fee based on the equation below per job:
𝐶(𝑥) = 60 + 20𝑥 + 2𝑥 2
1. Fill in the data table below for the following values 𝑥 = 0, 1, 2, 3, 4, 𝑎𝑛𝑑 5
x
0
1
2
3
4
5
𝑪(𝒙)
2. Graph the data table.
3. What does the value at 𝐶(0) mean?
4. What does the graph and data table tell us
about the longer Ray is working on the same
job?
5. What is the value if Ray is working there all
day (8 hour work day)?
6. Should the points be connected? Why or
Why not?
7. Find k(–7), using the equation:
k(x) = – x – 14
8. Evaluate:
9. Check the solution to the following:
5𝑚 − 23 = −37; 𝑚 = −3
10. Solve for x.
f(y) = 6y – 2
for f(3)
6𝑥 − 3 = 21
11. Convert:
18 𝑘𝑚
3 ℎ𝑜𝑢𝑟
to
𝑚
𝑠𝑒𝑐
Homework Unit 2 Day 5
Name: ________________________________
You have decided to take Claire’s idea and use it at your house. Your dad brings home 20 pieces
of fencing, and he will not let you cut them. Using this information, answer the following
questions:
1. Make a table for all the possible integer values that the garden can have:
x
y
2. Graph the possible dimensions of your garden.
3. Did you consider x = 10? Why or Why not?
4. What is the maximum value that you can
have for your garden at home?
1
5. Evaluate:
f(x) = 34 + 4x for f(6)
6. Find f (2), using the equation:
f(x) = 6x – 1
7. Check the solution to the following:
3𝑥 + 15 = 9; 𝑥 = −2
8. Is 𝑥 = 4 a solution to the equation:
3
𝑥 + 12 = 15
4
9. Use order of Operations:
(2 + 3(6 − 4) ÷ 12)
10. Combine like terms:
2x3 – 3x2 + 5x2 – 4x3 +7x
Homework Unit 2 Day 6
Name: ________________________________
Bob has 18 pieces of fencing with which to enclose his rectangle garden. Like Claire, he cannot
cut any of the panels.
1. Use function notation to write the formula for the area of the garden in terms of 𝑥.
𝐺(𝑥) = _____________________________
2. Using the equation above, fill in the data table.
x
𝑮(𝒙)
3. Using the table above, What is the domain
of the function? What is the range of the
function?
4. If Bob wanted to build the garden with the
largest possible area, what dimensions would
he use? How do you know?
5. Evaluate:
𝑓(𝑥) = 2𝑥 + 15 for 𝑓(3)
6. Solve for x.
3𝑥 + 8 = 15
7. Combine like terms:
3𝑥 + 2𝑦 − 5𝑥 + 12𝑦 − 42
8. Charlotte is making cookies for her friends,
but she doesn’t want to make a full batch. She
1
only wants to make 4 of the cookies that the
recipe normally makes. If the recipe calls for 3
cups of sugar, how much sugar does she need?
9. Convert:
20 miles per hour to feet per second.
Homework Unit 2 Day 7
Name: ________________________________
Cam had 32 feet of fencing with which to enclose her rectangle garden. Cam decides that she is
going to cut her fencing.
1. Use function notation to write the formula for the area of the garden in terms of 𝑥.
𝐺(𝑥) = _____________________________
2. Using the equation above, finish the data table below.
x
1
2
3
𝑮(𝒙)
15
28
39
4
5
6
7
3. Graph the data table.
4. Are the dots supposed to be connected? Why 5. What is the domain and range of the
or Why not?
function?
6. Evaluate 𝑓(𝑥) = 5𝑥 + 1 for 𝑓(2)
7. Simplify.
12 + 6 ÷ 3 − 2
8. Solve for x.
−7𝑥 + 17 = −4
9. Translate the phrase into an algebraic
expression, equation, or inequality:
Six minus 4 times a number y.
10. You plan to ride your bicycle to school and back at an average rate of 6 miles per hour for a
distance of 10.5 miles how long will it take you?
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 𝑟𝑎𝑡𝑒 ∙ 𝑡𝑖𝑚𝑒
Homework Unit 2 Day 8
1. Are the following sequences finite or
infinite?
a. 5, 25, 125, 625, …
Name: ________________________________
2. What pattern do you see in the following
sequence?
3, 6, 9, 12, ….
b. 2, 4, 6, 8
3. Match the sequence with the correct recursive rule:
a) 4, 7, 10, 13, 16, …
I.
𝑎1 = 3, 𝑎𝑛 = 3 ∙ 𝑎𝑛−1
b) 3, 7, 11, 15, …
II.
𝑎1 = 3, 𝑎𝑛 = 𝑎𝑛−1 + 4
c) 2, 4, 6, 8, …
III.
𝑎1 = 2, 𝑎𝑛 = 𝑎𝑛−1 + 2
d) 3, 9, 27, 81, ….
IV.
𝑎1 = 4, 𝑎𝑛 = 𝑎𝑛−1 + 3
a) 4, 7, 10, 13, 16, …
I.
𝑎𝑛 = 2𝑛
b) 3, 7, 11, 15, …
II.
𝑎𝑛 = 3𝑛
c) 2, 4, 6, 8, …
III.
𝑎𝑛 = 3𝑛 + 1
d) 3, 9, 27, 81, …
IV.
𝑎𝑛 = 4𝑛 − 1
4. Match the sequence with the correct explicit rule:
1. Evaluate:
a. −2 + 14
2. Evaluate the expressions using Order of
Operations:
a. [(7 − 4)2 + 3] + 1
b. 6 − 15
c. −10 + 19
b. 6(5 − 3)2 + 3
d. 9 + 5
3. Write the verbal phrase as an algebraic 4. Which of the following is a function? (circle all
expression, equation, or inequality:
that apply) Why?
Three times the quantity two less than a
number 𝑥 is ten.
5. Solve for x:
4𝑥 − 8 = 24
a)
Input
1
2
3
4
output
3
6
11
18
b)
Input
9
9
8
7
Output
5
4
3
2
c)
Input
2
2
4
5
output
3
4
5
6
6. Jodie got a job babysitting for her aunt. Her aunt
has her come over twice a week for 3 hours each time
(6 hours per week). Her aunt told her she would pay
her $72 every 2 weeks. How much does Jodie get
paid every hour?
Homework Unit 2 Day 9
Name: ________________________________
1. Given the table below what is the domain
and range?
Input
Output
1
-5
2
-8
3
-11
2. What pattern do you see between the inputs
and outputs in number #1? (As x increases how
does y change, and by how much?)
Domain: __________________________
Range: ____________________________
3. Write an equation for the table in #1.
(y = mx + b)
4. Using the equation in #3, what is the output
when the input is 12?
5. Evaluate:
6. State whether each of the following is an
expression, an equation, or an inequality:
a) 3𝑥 + 1 = 14
b) 3𝑥 + 2 ≤ 8
3𝑥 + 4 when 𝑥 = 5
c)
7. Is 𝑥 = 14 a solution to the equation:
3𝑥 + 2 = 45?
9𝑦 − 5
d) 5(𝑦 2 + 4) − 7
8. Translate the phrase into an algebraic
expression, equation, or inequality:
The quotient of an unknown number and six is
negative thirty-six.
9. You plan to ride your bicycle to school and back at an average rate of 8 miles per hour for a
distance of 4 miles how long will it take you?
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 𝑟𝑎𝑡𝑒 ∙ 𝑡𝑖𝑚𝑒
10. Convert:
2600
𝑓𝑡
= ____________𝑚𝑝ℎ
𝑚𝑖𝑛
Homework Unit 2 Day 10
Name: ________________________________
1. A car drives 80 miles in 2 hours and 200
miles in 5 hours, what is the average speed?
2. Lebron James scored 6 points after 18
minutes and scored a total of 39 points by the
end of the game (48 minutes).
a) What is the average amount of points he
scored per minute during the first 18 minutes
of the game?
b) What is the average amount of points he
scored per minute during the entire game?
3. Troy is 29 inches tall when he is 1 year old
and 66 inches tall when he is 15 years old,
what is the average rate at which he grew over
the years?
4. Kyle was driving home to Tucson from his
grandma’s house in Glendale (110 miles
away), he left at 3pm, he arrived at his house at
5 pm. What was his average speed on his drive
home?
5. Use order of operations:
2[(9 − 8)2 + (12 − 5)2 ]
6. Evaluate:
a. −2 + (−6)
b. −2 + 6
2−6
d. 2 + 6
c.
7. Solve for x:
2𝑥 + 10 = 4
9. Evaluate:
1
𝑓(𝑥) = − 2 𝑥 + 10 for 𝑓(𝑥) = 8
8. Evaluate:
𝑓(𝑥) = 4𝑥 − 3 for 𝑥 = 3
10. Translate the following phrase into an
algebraic equation, then solve the equation.
Four less than a number is six more than two
times that same number.
11. If you go to school for 180 days each school year and each school day is 7 hours long, how
many hours are spent in school in one school year?
Homework Unit 2 Day 11
Name: ________________________________
1. Given the sequence: 2, 4, 8, 16, 32, …
2. Write a function for the sequence in #1.
a. What is the next term?
b. What is the pattern that you see?(in a
sentence)
3. At noon yesterday the classroom
thermometer read 78℉ at 2:30 pm yesterday,
the thermometer also read 78℉. What is the
average rate of change in temperature?
4. Denise is starting a diet. In her 3rd week, her
weight is 142 pounds. In her 8th week, her
weight is 122 pounds. What is the rate of
change for her weight?
5. Convert:
8
miles per hour to feet per second
6. A monkey ran 30 feet in 4 seconds. What was the monkey’s average speed in miles per hour?
7. Evaluate:
a. −16 + (−2)
c.
8. Solve for x:
b. (−2) − 3
−2(−3)
d. 5 − 9
9. What is the domain and range for the
following table?
x
y
1
2
Domain =
Range =
3
4
8𝑥 − 7 = 17
5
6
7
8
10. Is 𝑥 = −5 a solution to the equation
3𝑥 + 2 = 13
Homework Unit 2 Day 12
Name: ________________________________
1. Match the graphs to their equations:
𝐴. 𝑓(𝑥) = 𝑥 2 − 8𝑥 + 13
𝐶.
𝑓(𝑥) =
𝐵.
7
𝑥−2
2
I.
𝑓(𝑥) = −6𝑥 + 3
1
𝐷. 𝑓(𝑥) = − 𝑥 2
2
II.
Equation ________________________
III.
Equation ________________________
Equation ________________________
IV.
Equation ________________________
2. Evaluate:
a. 7[(18 − 6) − 6]
3. Combine like terms:
a.
9 − 3𝑥 − (−8𝑦) + 9𝑥 − 𝑦
b. 6(5 − 3) + 3
b.
2𝑦 + 3𝑦 − (12𝑥) − 7𝑥 + 2𝑥𝑦
c. (−12) + (−11)
4. Solve for x:
3𝑥 + 7 = 16
5. Label the following expression, inequality,
or equation.
a. 3𝑥 + 2 = 4
b. 4𝑦 − 7 < 9
c. 5 ≠ 4𝑥 + 3
6. Let’s suppose you drop a rock from the Leaning Tower of Pisa. If the rock is falling at a rate
of 62 feet per second, how many miles per hour is it falling?
7. Bamboo is one of the fastest growing plants. It is used to create paper, clothing, building
materials, etc. John measured the bamboo plant at 1pm and it was 21 inches tall. At 5 pm, he
measured the plant again and it was 33 inches. What is the rate of change?