Name______________________________
Date: _________________
Algebra 1 Review - Lesson 1
1. The data in the table below are graphed, and the slope is examined.
The rate of change represented in this table can be described as
(1) negative
(3) undefined
(2) positive
(4) zero
2. Given the functions g(x), f(x), and h(x) shown below:
The correct list of functions ordered from greatest to least by average rate of change over the
interval is 0  x  3 is
1
(1) f(x), g(x), h(x)
(3) g(x), f(x), h(x)
(2) h(x), g(x), f(x)
(4) h(x), f(x), g(x)
3. A turtle and a rabbit are in a race to see who is first to reach a point 100 feet away. The turtle
travels at a constant speed of 20 feet per minute for the entire 100 feet. The rabbit travels at
a constant speed of 40 feet per minute for the first 50 feet, stops for 3 minutes, and then
continues at a constant speed of 40 feet per minute for the last 50 feet.
Determine which animal won the race and by how much time.
4. During a snowstorm, a meteorologist tracks the amount of accumulating snow. For the first
three hours of the storm, the snow fell at a constant rate of one inch per hour. The storm
then stopped for two hours and then started again at a constant rate of one-half inch per hour
for the next four hours.
a) On the grid below, draw and label a graph that models the accumulation of snow over
time using the data the meteorologist collected.
b) If the snowstorm started at 6 p.m., how much snow had accumulated by midnight?
2
5. Albany begins the day with 5 inches of snow on the ground and Buffalo begins the same day
with 2 inches of snow on the ground. Two snowstorms begin at the same time in Albany and
Buffalo, snowing at a rate of 0.8 inches per hour in Albany and 1.4 inches per hour in
Buffalo. The number of inches of snow on the ground in Albany and Buffalo during the
course of these snowstorms are modeled by f(x) and g(x), respectively.
f x   0.8 x  5
g x   1.4 x  2
Determine the number of hours (x) that would pass before Albany and Buffalo have the same
amount of snow on the ground. [The use of the grid below is optional.]
y
x
3
6. Solve 8m 2  20m  12 for m by factoring.
7. About a year ago, Joey watched an online video of a band and noticed that it had been viewed
only 843 times. One month later, Joey noticed that the band’s video had 1,708 views. Joey
made the table below to keep track of the cumulative number of views the video was getting
online.
Months since 1st Viewing
Total Views
0
843
1
1,708
2
Forgot to record
3
7,124
4
14,684
5
29,787
6
62,381
a) Write a regression equation that best models these data. Round all values to the nearest
hundredth. Justify your choice of regression equation.
b) As shown in the table, Joey forgot to record the number of views after the second
month. Use the equation from part a to estimate the number of full views of the online
video that Joey forgot to record.
4
Name: _____________________
Date: _________________
Algebra Review – Lesson 2
1
1. Which ordered pair is not in the solution set of y   x  5 and y  3 x  2 ?
2
(1) (5, 3)
(3) (4, 3)
(2) (3, 4)
(4) (4, 4)
2. The equation y  x 2  3x  18 is graphed on the set of axes below.
Based on this graph, what are the roots of the equation x 2  3x  18  0 ?
(1) -3 and 6
5
(2) 0 and -18
(3) 3 and -6
(4) 3 and -18
3. The graphs below represent functions defined by polynomials.
For which function are the zeros of the polynomials 2 and –3?
6
(1)
(3)
(2)
(4)
4. The table below, created in 1996, shows a history of transit fares from 1955 to 1995. On the
grid below, construct a scatter plot where the independent variable is years. State the
exponential regression equation with the coefficient and base rounded to the nearest
thousandth. Using this equation, determine the prediction that should have been made for the
year 1998, to the nearest cent.
y
x
7
5. Max purchased a box of green tea mints. The nutrition label on the box stated that a serving of
three mints contains a total of 10 Calories.
On the axes below, graph the function, C, where C (x) represents the number of Calories in
x mints.
Write an equation that represents C (x).
A full box of mints contains 180 Calories. Use the equation to determine the total number of
mints in the box.
8
6. The table below lists the total cost for parking for a period of time on a street in Albany, N.Y.
The total cost is for any length of time up to and including the hours parked. For example,
parking for up to and including 1 hour would cost $1.25; parking for 3.5 hours would cost
$5.75.
Graph the step function that represents the cost for the number of hours parked.
Explain how the cost per hour to park changes over the six-hour period.
9
7. The diagram below, when completed, shows all possible ways to build equivalent expressions
of 3x2 using multiplication. The equivalent expressions are connected by labeled segments
stating which property of operations, A for Associative and C for Commutative Property,
justifies why the two expressions are equivalent.
a) Fill in the empty circles with A or C and the empty rectangle with the missing expression
to complete the diagram.
b) Using the diagram above to help guide you, give two different proofs that
x  x  3  3  x  x .
10
8. A father divided his land so that he could give each of his two sons a plot of his own and keep
a larger plot for himself. The sons’ plots are represented by squares #1 and #2 in the figure
below. All three shapes are squares. The area of square #1 equals that of square #2 and each can
be represented by the expression 4 x 2  8 x  4 .
a. Find the side length of the father’s plot, square #3, and show or explain how you found it.
b. Find the area of the father’s plot and show or explain how you found it.
c. Find the total area of all three plots by adding the three areas and verify your answer by
multiplying the outside dimensions. Show your work.
11
Name: _____________________
Date: _________________
Algebra Review Lesson 3
1. If n is an odd integer, which equation can be used to find three consecutive odd integers
whose sum is -3?
(1) n + (n + 1) + (n + 3) = -3
(3) n + (n + 2) + (n + 4) = -3
(2) n + (n + 1) + (n + 2) = -3
(4) n + (n + 2) + (n + 3) = -3
2. The length of the shortest side of a right triangle is 8 inches. The lengths of the other two
sides are represented by consecutive odd integers. Which equation could be used to find the
lengths of the other sides of the triangle?
(1) 8 2  x  1  x 2
(2) x 2  8 2   x  1
(3) 8 2  x  2  x 2
2
2
(4) x 2  8 2  x  2
2
3. Emma recently purchased a new car. She decided to keep track of how many gallons of gas
she used on five of her business trips. The results are shown in the table below.
Write the linear regression equation for this data where miles driven is the independent
variable. (Round all values to the nearest hundredth.)
12
4. A model rocket is launched from a platform in a flat, level field and lands in the same field.
The height of the rocket follows the function, f x   16 x 2  150 x  5 , where f(x) is the
height, in feet, of the rocket and x is the time, in seconds, since the rocket is launched.
Determine the maximum height, to the nearest tenth of a foot, the rocket reaches.
Determine the length of time, to the nearest tenth of a second, from when the rocket is
launched until it hits the ground. [The use of the grid below is optional.]
y
x
13
5. Solve for x in each of the equations/inequalities below. If appropriate write identity or no
solution. Name the property and/or properties used.
a)
3
x9
4
c) a  x  b
14
b) 10  5x  5x
d) cx  d
e)
1
xg m
2
f) q  5 x  5 x  q
g)
3
x  2  6x  12
4
h) 35  5x  5x
6. Suppose that Peculiar Purples and Outrageous Oranges are two different and unusual types of
bacteria. Both types multiply through a mechanism in which each single bacterial cell splits
into four. However, they split at different rates: Peculiar Purples split every 12 minutes,
while Outrageous Oranges split every 10 minutes.
a. If the multiplication rate remains constant throughout the hour and we start with three bacterial
cells of each, after one hour, how many bacterial cells will there be of each type? Show your
work and explain your answer.
b. If the multiplication rate remains constant for two hours, which type of bacteria is more
abundant? What is the difference between the numbers of the two bacterial types after two
hours?
c. Write a function to model the growth of Peculiar Purples and explain what the variable and
parameters represent in the context.
15
d. Use your model from part (c) to determine how many Peculiar Purples there will be after three
splits, i.e., at time 36 minutes. Do you believe your model has made an accurate prediction? Why
or why not?
e. Write an expression to represent a different type of bacterial growth with an unknown initial
quantity but in which each cell splits into 2 at each interval of time.
7. Consider the following system of equations with the solution x = 3, y = 4.
Equation A1: y  x  1
Equation A2: y  2 x  10
Write a unique system of two linear equations with the same solution set. This time make
both linear equations have positive slope.
Equation B1: ________________
Equation B2: ________________
16
Name: _____________________
Date: _________________
Algebra Review - Lesson 4
1. If the quadratic formula is used to find the roots of the equation x 2  6 x  19  0 , the correct
roots are
(1) 3  2 7
(3) 3  4 14
(2)  3  2 7
(4)  3  4 14
2. Chelsea has $45 to spend at the fair. She spends $20 on admission and $15 on snacks. She
wants to play a game that costs $0.65 per game. Write an inequality to find the maximum
number of times, x, Chelsea can play the game.
Using this inequality, determine the maximum number of times she can play the game.
3. Donna wants to make trail mix made up of almonds, walnuts and raisins. She wants to mix
one part almonds, two parts walnuts, and three parts raisins. Almonds cost $12 per pound,
walnuts cost $9 per pound, and raisins cost $5 per pound.
Donna has $15 to spend on the trail mix. Determine how many pounds of trail mix she can
make. [Only an algebraic solution can receive full credit.]
17
4. The table below shows the relationship between the length of a person’s foot and the length of
his or her stride.
Write the linear regression equation for this set of data, rounding all values to the nearest
hundredth.
Using the linear correlation coefficient, explain how accurate this function is in predicting a
person’s stride length.
Predict the stride length, in inches, of a person whose foot measures 8 inches.
18
5. On the set of axes below, graph the function represented by y  3 x  2 for the domain
 6  x  10 .
y
x
19
6. Use the data below to write the regression equation ( y  ax  b ) for the raw test score based
on the hours tutored. Round all values to the nearest hundredth.
Equation: ____________________________________________________
Create a residual plot on the axes below, using the residual scores in the table above.
Based on the residual plot, state whether the equation is a good fit for the data.
Justify your answer.
20
7. The figures below show the first four steps of making Sierpinski’s Triangle.
a. What fraction of each figure is shaded?
b. Use your answer from part (a) to write a function rule which relates the step number to the
fraction of the figure that is shaded.
c. What fraction of step 6 would be shaded?
d. What fraction of each step is NOT shaded?
e. Write a function rule which relates the step number to the fraction which is NOT shaded.
f. What fraction of step 8 is not shaded?
21
8. Compare the following three functions:
i. A function f is represented by the graph below:
ii. A function g is represented by the following equation:
2
g x   x  6  36
iii. A linear function h is represented by the following table:
For each of the following, evaluate the three expressions given and identify which expression has
the largest value and which has the smallest value. Show your work.
a. f 0, g 0, h0
b.
22
f 4  f 2
42
g 4  g 2
42
h4  h2
42
Name: _____________________
Date: _________________
Algebra Review – Lesson 5
1. Which statistic would indicate that a linear function would not be a good fit to model a data
set?
23
(1) r  0.93
(3) r  1
(2) Residual
(4) Residual
2. The cost of 3 markers and 2 pencils is $1.80. The cost of 4 markers and 6 pencils is $2.90.
What is the cost of each item? Include appropriate units in your answer.
3. A high school drama club is putting on their annual theater production. There is a maximum
of 800 tickets for the show. The costs of the tickets are $6 before the day of the show and $9
on the day of the show. To meet the expenses of the show, the club must sell at least $5,000
worth of tickets.
a) Write a system of inequalities that represent this situation.
b) The club sells 440 tickets before the day of the show. Is it possible to sell enough
additional tickets on the day of the show to at least meet the expenses of the show? Justify
your answer.
24
4. The function f x  is given below.
f x   x 2  2 x  3
Describe the effect on the graph of f x  , if g x  f x  5 .
Show that the vertices of f x  and g x support your description.
[The use of the set of axes below is optional.] (GC 2 – AU2/9)
y
x
25
5.
The diagram below shows how tables and chairs are arranged in the school cafeteria. One
table can seat 4 people, and tables can be pushed together. When two tables are pushed
together, 6 people can sit around the table.
a.
Complete this table to show the relationship between the number of tables, 𝑛, and the
number of students, 𝑆, that can be seated around the table.
b.
If we made a sequence where the first term of the sequence was the number of students
that can fit at 1 table, the 2nd term where the number that could fit at 2 tables, etc, would
the sequence be arithmetic? Explain your reasoning.
c.
Create an explicit formula for a sequence that models this situation. Use n = 1 as the first
term, representing how many students can sit at 1 table. How do the constants in your
formula relate to the situation?
d.
Using this seating arrangement, how many students could fit around 15 tables pushed
together in a row?
Name: _____________________
Date: _________________
Algebra Review – Lesson 6
1. Which equation has roots of -3 and 5? (RJa11#28 – AU7)
26
(1) x 2  2 x  15  0
(3) x 2  2 x  15  0
(2) x 2  2 x  15  0
(4) x 2  2 x  15  0
2. For which function defined by a polynomial are the zeros of the polynomial -4 and -6?
(1) y  x 2  10 x  24
(3) y  x 2  10 x  24
(2) y  x 2  10 x  24
(4) y  x 2  10 x  24
3. David has two jobs. He earns $8 per hour babysitting his neighbor’s children and he earns $11
per hour working at the coffee shop.
Write an inequality to represent the number of hours, x, babysitting and the number of
hours, y, working at the coffee shop that David will need to work to earn a minimum of
$200.
David worked 15 hours at the coffee shop. Use the inequality to find the number of full
hours he must babysit to reach his goal of $200.
27
4. At an office supply store, if a customer purchases fewer than 10 pencils, the cost of each
pencil is $1.75. If a customer purchases 10 or more pencils, the cost of each pencil is $1.25.
Let c be a function for which c (x) is the cost of purchasing x pencils, where x is a whole
number.
1.75 x, if 0  x  9
c x   
1.25 x, if x  10
Create a graph of c on the axes below.
A customer brings 8 pencils to the cashier. The cashier suggests that the total cost to
purchase 10 pencils would be less expensive. State whether the cashier is correct or
incorrect. Justify your answer.
28
5. The box plots below display the distributions of maximum speed for 145 roller coasters in the
United States, separated by whether they are wooden coasters or steel coasters.
Based on the box plots, answer the following questions or indicate whether you do not have
enough information.
a. Which type of coaster has more observations?
A. Wooden
B. Steel
C. About the same
Explain your choice:
D. Cannot be determined
b. Which type of coaster has a higher percentage of coasters that go faster than 60mph?
A. Wooden
B. Steel
C. About the same
D. Cannot be determined
Explain your choice:
c. Which type of coaster has a higher percentage of coasters that go faster than 50 mph?
A. Wooden
B. Steel
C. About the same
D. Cannot be determined
Explain your choice:
d. Which type of coaster has a higher percentage of coasters that go faster than 48 mph?
A. Wooden
B. Steel
C. About the same
D. Cannot be determined
Explain your choice:
e. Write 2–3 sentences comparing the two types of coasters with respect to which type of coaster
tends to go faster.
29
6. Sydney was studying the following functions:
f x  2x  4 and g x   22 x   4
She said that linear functions and exponential functions are basically the same. She made
her statement based on plotting points at x  0 and x  1 and graphing the functions.
Help Sydney understand the difference between linear functions and exponential functions
by comparing and contrasting f and g. Support your answer with a written explanation that
includes use of the average rate of change and supporting tables and/or graphs of these
functions.
30
7. The table shows the average sale price 𝑝 of a house in New York City, for various years t
since 1960.
a. What type of function most appropriately represents this set of data? Explain your reasoning.
b. In what year is the price at the lowest? Explain how you know.
c. Write a function to represent the data. Show your work.
d. Can this function ever be equal to zero? Explain why or why not.
e. Mr. Samuels bought his house in New York City in 1970. If the trend continued, how much
was he likely to have paid? Explain and provide mathematical evidence to support your answer.
31
The cafeteria needs to provide seating for 189 students. They can fit up to 15 rows of tables in
the cafeteria. Each row can contain at most 9 tables but could contain less than that. The tables
on each row must be pushed together. Students will still be seated around the tables as described
earlier.
e.
If they use exactly 9 tables pushed together to make each row, how many rows will they
need to seat 189 students, and how many tables will they have used to make those rows?
f.
Is it possible to seat the 189 students with fewer total tables? If so, what is the fewest
number of tables needed? How many tables would be used in each row? (Remember that
the tables on each row must be pushed together.) Explain your thinking.
32
6. A rectangle with positive area has length represented by the expression 3x 2  5 x  8 and width
by 2 x 2  6 x . Write expressions in terms of x for the perimeter and area of the rectangle. Give
your answers in standard polynomial form and show your work.
a. Perimeter:
b. Area:
c. Are both your answers polynomials? Explain why or why not for each.
d. Is it possible for the perimeter of the rectangle to be 16 units? If so what value(s) of x will
work? Use mathematical reasoning to explain how you know you are correct.
33
e. For what value(s) of the domain will the area equal zero?
f. The problem states that the area of the rectangle is positive. Find and check two positive
domain values that will produce a positive area.
g. Is it possible that negative domain values could produce a positive function value (area)?
Explain why or why not in the context of the problem.
34
7. Label each graph with the function it represents; choose from those listed below:
f x   3 x
k x   x  2  1
35
g x  
13
x
2
m x   3 x  2
hx   5 x 2
nx   x  3  1
2
Name: _____________________
Date: _________________
Algebra Review – Lesson 7
1 2
x  4 . He wants to find the zeros of the
2
function, but is unable to read them exactly from the graph.
1. Ryker is given the graph of the function y 
Find the zeros in simplest radical form.
36
2. Next weekend Marnie wants to attend either carnival A or carnival B. Carnival A charges $6
for admission and an additional $1.50 per ride. Carnival B charges $2.50 for admission and
an additional $2 per ride.
a) In function notation, write A(x) to represent the total cost of attending carnival A and
going on x rides. In function notation, write B(x) to represent the total cost of attending
carnival B and going on x rides.
b) Determine the number of rides Marnie can go on such that the total cost of attending each
carnival is the same. [Use of the set of axes below is optional.]
c) Marnie wants to go on five rides. Determine which carnival would have the lower total
cost. Justify your answer.
y
x
37
3. On the set of axes below, graph the function y  x  1 .
y
x
State the range of the function.
State the domain over which the function is increasing.
38
4. The population of a remote island has been experiencing a decline since the year 1950.
Scientists used census data from 1950 and 1970 to model the declining population. In 1950
the population was 2350. In 1962 the population was 1270. They chose an exponential
x
decay model and arrived at the function: px   23500.95 , x  0 , where x is the number
of years since 1950. The graph of this function is given below.
a. What is the y-intercept of the graph? Interpret its meaning in the context of the problem.
b. Over what intervals is the function increasing? What does your answer mean within the
context of the problem?
c. Over what intervals is the function decreasing? What does your answer mean within the
context of the problem?
39
Another group of scientists argues that the decline in population would be better modeled by a
linear function. They use the same two data points to arrive at a linear function.
d. Write the linear function that this second group of scientists would have used.
e. What is the x-intercept of the function? Interpret its meaning in the context of the problem.
f. Graph the function on the coordinate plane.
g. What is an appropriate domain for the function? Explain your choice within the context of the
problem.
40
5. The physician’s health study examined whether physicians who took aspirin were less likely
to have heart attacks than those who took a placebo (fake) treatment. The table below shows
their findings.
Based on the data in the table, what conclusions can be drawn about the association between
taking aspirin and whether or not a heart attack occurred? Justify your conclusion using the
given data.
41
6. Consider the equation x 2  2 x  6  y  2 x  15 and the function f x   4 x 2  16 x  84 in the
following questions:
a. Show that the graph of the equation x 2  2 x  6  y  2 x  15 has x-intercepts at x  3
and 7.
b. Show that the zeroes of the function f x   4 x 2  16 x  84 are the same as the x values
of the x-intercepts for the graph of the equation in part (a).
c. Explain how this function is different from the equation in part (a).
d. Identify the vertex of the graphs of each by rewriting the equation and function in the
2
completed-square form, a  x  h   k . Show your work. What is the same about the two
vertices? How are they different? Explain why there is a difference.
42
Name: _____________________
Date: _________________
Algebra Review – Lesson 8
1. A local business was looking to hire a landscaper to work on their property. They narrowed
their choices to two companies. Flourish Landscaping Company charges a flat rate of $120
per hour. Green Thumb Landscapers charges $70 per hour plus a $1600 equipment fee.
Write a system of equations representing how much each company charges.
Determine and state the number of hours that must be worked for the cost of each company
to be the same. [The use of the grid below is optional.]
If it is estimated to take at least 35 hours to complete the job, which company will be less
expensive? Justify your answer.
43
2. Sam says that he knows a clever set of steps to rewrite the expression:
x  33x  8  3xx  3
as a sum of two terms where the steps don’t involve multiplying the linear factors first and
then collecting like terms.
Rewrite the expression as a sum of two terms (where one term is a number and the other is a
product of a coefficient and variable) using Sam’s steps if you can. (M1:MM#4 – AU7)
3. If a  0 and c  b , circle the expression that is greater:
ab  c or ac  b
Use the properties of inequalities to explain your choice.
44
4. A recent social survey asked 654 men and 813 women to indicate how many “close friends”
they have to talk about important issues in their lives. Below are frequency tables of the
responses.
a. The shape of the distribution of the number of close friends for the males is best characterized
as:
A. Skewed to the higher values (right or positively skewed)
B. Skewed to the lower values (left or negatively skewed)
C. Symmetric
b. Calculate the median number of class friends for the females. Show your work.
c. Do you expect the mean number of close friends for the females to be larger or smaller than
the median you found in (b) or do you expect them to be the same? Explain your choice.
d. Do you expect the mean number of close friends for the males to be larger or smaller than the
mean number of close friends for the females or do you expect them to be the same? Explain
your choice.
45
5. In their entrepreneurship class, students are given two options for ways to earn a commission
selling cookies. For both options, students will be paid according to the number of boxes
they are able to sell, with commissions being paid only after all sales have ended. Students
must commit to one commission option before they begin selling.
Option 1: The commission for each box of cookies sold is 2 dollars.
Option 2: The commission will be based on the total number of boxes of cookies sold as follows:
2 cents is the total commission if one box is sold, 4 cents is the commission if two
boxes are sold, 8 cents if three boxes are sold, and so on, doubling the amount for each
additional box sold. (This option is based upon the total number of boxes sold and is
paid on the total, not each individual box.)
a. Define the variables and write function equations to model each option.
Describe the domain for each function.
b. If Barbara thinks she can sell five boxes of cookies, should she choose Option 1 or 2?
c. Which option should she choose if she thinks she can sell ten boxes? Explain.
46
d. How many boxes of cookies would a student have to sell before Option 2 pays more than
Option 1? Show your work and verify your answer graphically.
47
6. Let f and g be the functions given by f x   x 2 and g x   x x .


1
a. Find f  , g 4  , and g  3 .
3
b. What is the domain of f?
c. What is the range of g?
d. Evaluate f  67  g  67 .
e. Compare and contrast f and g. How are they alike? How are they different?
f. Is there a value of x, such that f x  g x  100 ? If so, find x. If not, explain why no such
value exists.
g. Is there a value of such that f x  g x  50 ? If so, find x. If not, explain why no such value
exists. x
48
7. Veronica’s physics class is analyzing the speed of a dropped object just before it hits the
ground when it’s dropped from different heights. They are comparing the final velocity, in
feet/second, versus the height, in feet, from which the object was dropped. The class comes up
with the following graph.
a. Use transformations of the parent function, f  x   x , to write an algebraic equation that
represents this graph. Describe the domain in terms of the context.
b. Veronica and her friends are planning to go cliff diving at the end of the school year. If she
dives from a position that is 165 ft. above the water, at what velocity will her body be moving
right before she enters the water? Show your work and explain the level of precision you chose
for your answer.
c. Veronica’s friend, Patrick, thinks that if she were able to dive from a 330-ft. position, she
would experience a velocity that is twice as fast. Is he correct? Explain why or why not.
49
8. The tables below represent values for two functions, f and g, one absolute value and one
quadratic.
a. Label each function as either absolute value or quadratic. Then explain mathematically how
you identified each type of function.
b. Represent each function graphically. Identify and label the key features of each in your graph
(e.g., vertex, intercepts, axis of symmetry, etc.).
y
y
x
c. Represent each function algebraically.
50
x
Name: _____________________
Date: _________________
Algebra Review – Lesson 9
1. Students and adults purchased tickets for a recent basketball playoff game. All tickets were
sold at the ticket booth—season passes, discounts, etc. were not allowed.
Student tickets cost $5 each, and adult tickets cost $10 each.
A total of $4500 was collected. 700 tickets were sold.
a) Write a system of equations that can be used to find the number of student tickets, s, and
the number of adult tickets, a, that were sold at the playoff game.
b) Assuming that the number of students and adults attending would not change, how much
more money could have been collected at the playoff game if the ticket booth charged
students and adults the same price of $10 per ticket?
c) Assuming that the number of students and adults attending would not change, how much
more money could have been collected at the playoff game if the student price was kept at $5
per ticket and adults were charged $15 per ticket instead of $10?
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2. Weather data were recorded for a sample of 25 American cities in one year. Variables
measured included January high temperature (in degrees Fahrenheit), January low
temperature, annual precipitation (in inches), and annual snow accumulation. The
relationships for three pairs of variables are shown in the graphs below (Jan Low
Temperature – Graph A; Precipitation – Graph B; Annual Snow Accumulation – Graph C).
a. Which pair of variables will have a correlation coefficient closest to 0?
A. Jan high temperature and Jan low temperature
B. Jan high temperature and Precipitation
C. Jan high temperature and Snow accumulation
Explain your choice:
b. Which of the above scatterplots would be best described as a strong nonlinear relationship?
Explain your choice:
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3. Given hx   x  2  3 and g x    x  4 .
a. Describe how to obtain the graph of g from the graph of ax  x using transformations.
b. Describe how to obtain the graph of h from the graph of ax  x using transformations.
c. Sketch the graphs of hx  and g x on the same coordinate plane.
y
8
7
6
5
4
3
2
1
–8
–7
–6
–5
–4
–3
–2
–1
–1
1
2
3
4
5
6
7
8
x
–2
–3
–4
–5
–6
–7
–8
d. Use your graphs to estimate the solutions to the equation:
x  2 3  x  4
Explain how you got your answer.
e. Were your estimations you made in part (d) correct? If yes, explain how you know. If not
explain why not.
53
4. A boy bought 6 guppies at the beginning of the month. One month later the number of
guppies in his tank had doubled. His guppy population continued to grow in this same manner.
His sister bought some tetras at the same time. The table below shows the number of tetras, t,
after n months have passed since they bought the fish.
a. Create a function g to model the growth of the boy’s guppy population, where g(n) is the
number of guppies at the beginning of each month, and n is the number of months that have
passed since he bought the 6 guppies. What is a reasonable domain for g in this situation?
b. How many guppies will there be one year after he bought the 6 guppies?
c. Create an equation that could be solved to determine how many months after he bought the
guppies there will be 100 guppies.
d. Use graphs or tables to approximate a solution to the equation from part (c). Explain how you
arrived at your estimate.
y
x
54
e. Create a function, t, to model the growth of the sister’s tetra population, where t(n) is the
number of tetras after n months have passed since she bought the tetras.
f. Compare the growth of the sister’s tetra population to the growth of the guppy population.
Include a comparison of the average rate of change for the functions that model each
population’s growth over time.
g. Use graphs to estimate the number of months that will have passed when the population of
guppies and tetras will be the same.
y
x
h. Use graphs or tables to explain why the guppy population will eventually exceed the tetra
population even though there were more tetras to start with.
i. Write the function g(n) in such a way that the percent increase in the number of fish per month
can be identified. Circle or underline the expression representing percent increase in number of
fish per month.
55
5. The graph of a piecewise function f is shown to the right. The domain of f is  3  x  3 .
a. Create an algebraic representation for f. Assume that the graph of f is composed of straight line
segments.
b. Sketch the graph of y  2 f x  and state the domain and range.
y
6
5
4
3
2
1
–6
–5
–4
–3
–2
–1
–1
1
–2
–3
–4
–5
–6
c. How does the range of y  f x  compare to the range of y  kf x , where k  1 ?
56
2
3
4
5
6
x
d. Sketch the graph of y  f 2 x  and state the domain and range.
y
6
5
4
3
2
1
–6
–5
–4
–3
–2
–1
–1
1
2
3
–2
–3
–4
–5
–6
e. How does the domain of y  f x  compare to the domain of y  f kx , where k  1 ?
57
4
5
6
x
6. An arrow is shot into the air. A function representing the relationship between the number of
seconds it is in the air, t, and the height of the arrow in meters, h, is given by:
ht   4.9t 2  29.4t  2.5
a. Complete the square for this function.
b. What is the maximum height of the arrow? Explain how you know.
c. How long does it take the arrow to reach its maximum height? Explain how you know.
d. What is the average rate of change for the interval from t = 1 to t = 2 seconds? Compare your
answer to the average rate of change for the interval from t = 2 to t = 3 seconds and explain the
difference in the context of the problem.
58
e. How long does it take the arrow to hit the ground? Show your work or explain your answer.
f. What does the constant term in the original equation tell you about the arrow’s flight?
g. What do the coefficients on the second- and first-degree terms in the original equation tell you
about the arrow’s flight?
59
7. Rewrite each expression below in expanded (standard) form:

a. x  3


2

b. x  2 5 x  3 5

c. Explain why, in these two examples, the coefficients of the linear terms are irrational and why
the constants are rational.
Factor each expression below by treating it as the difference of squares:
d. q 2  8
e. t  16
8. Solve the following equations for r. Show your method and work.
If no solution is possible, explain how you know.
a. r 2  12r  18  7
60
b. r 2  2r  3  4
c. r 2  18r  73  9