(8) Lesson 4.5

1. Course 3, Lesson 4-5
Use the make a table strategy to solve Exercises 1 and 2.
1. Karl is going to increase the number of jumping jacks he does
each week by 5. If in the sixth week he is doing 85 jumping jacks,
how many jumping jacks will he do in the third week?
2. Anna has $25 in her piggy bank. She is planning on adding $2.50
to her bank each week. In how many weeks will she have saved
$42.50?
3. Neil has already collected a certain number of canned goods.
Each day he plans to collect 15 more cans. If by the fifth day he
has collected 165 cans, how many cans did he originally collect?

2. Course 3, Lesson 4-5
ANSWERS
1. 70
2. 7 weeks
3. 90

3. HOW can we model relationships
between quantities?
Functions
Course 3, Lesson 4-5

4. Course 3, Lesson 4-5 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council
of Chief State School Officers. All rights reserved.
Functions
• 8.F.2
Compare properties of two functions each represented in a different way
(algebraically, graphically, numerically in tables, or by verbal
descriptions).
• 8.F.4
Construct a function to model linear relationship between two quantities.
Determine the rate of change and initial value of the function from a
description of a relationship or from two (x, y) values, including reading
these from a table or from a graph. Interpret the rate of change and initial
value of a linear function in terms of the situation it models, and in terms
of its graph or a table of values.

5. Course 3, Lesson 4-5 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Functions
Mathematical Practices
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.

6. To
• compare two functions
represented in different forms
Course 3, Lesson 4-5
Functions

7. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
1. A zebra’s main predator is a lion. Lions can
run at a speed of 53 feet per second over
short distances. The graph at the right shows
the speed of a zebra. Compare their speeds.
To compare their speeds, compare the rates of change.
A zebra can travel at a rate of 59 feet per second. Since 59 > 53,
the speed of a zebra is greater than the speed of a lion.
A lion can travel at a rate of 53 feet per second.
To find the rate of change for a zebra, choose two points
on the line and find the rate of change between them.

8. Answer
Need Another Example?
The flow rate of water in a water
garden is 52 gallons per minute.
The graph shows the flow rate of
water in a Koi pond. Compare
the functions by comparing their
rates of change.
The water garden has a flow rate of 52 gallons
per minute and the Koi pond has flow rate of 60
gallons per minute. The water in the Koi pond
has a greater rate of change.

9. 1
Need Another Example?
2
3
4
5 6
Step-by-Step Example
2. The function m = 140h, where m is the miles traveled in h hours,
represents the speed of the first Japanese high speed train. The
speed of a high speed train operating today in China is shown in the
table. Assume the relationship between the two quantities is linear.
Compare the y-intercepts.
Since 217 > 140, the function representing the Chinese high speed
train has a greater rate of change than the function representing the
Japanese high speed train.
Compare the rates of change.
Use the table to find the speed of the Chinese train.
a. Compare the functions’ y-intercepts and rates of change.
The speed of the Chinese train is or 217 miles per hour.
Find the distance on the
Japanese train.
m = 140h
m = 140(5)
m = 140h
Write the function.
Replace h with 5.
Simplify.
b. If you ride each train for 5 hours, how far will you travel on each?
7 You will travel 700 miles in 5 hours on the Japanese train.
Find the distance on the Chinese train by extending the table.
You will travel 1,085 miles in 5 hours on the Chinese train.
At 0 hours, no distance has been covered.
So, the y-intercepts are the same, 0.
The speed of the Japanese train is 140 miles per hour.

10. Answer
Need Another Example?
A bowling alley offers different birthday party
packages. Package A is represented by the
function c = 7p + 5, where c is the total cost
and p is the number of people. Package B is
represented in the table to the right.
a.
b.
Compare the functions by comparing their
y-intercepts and rates of change.
How much more will Package B cost than
Package A if there are 12 people at the
birthday party?
The function for Package A has a y-intercept of 5
and the function for Package B has a y-intercept
of 0. Package A costs $7 per person and
Package B costs $9 per person. The rate of
change for Package B is greater.
$19 more

11. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
3. Financial Literacy Angela and Benjamin each have a monthly
cell phone bill. Angela’s monthly cell phone bill is represented
by the function y = 0.15x + 49, where x represents the minutes
and y represents the cost. Benjamin’s monthly cost is shown
in the graph.
The rate of change for Angela’s monthly bill is $0.15 per minute.
Find the rate of change for Benjamin's bill.
a. Compare the y-intercepts and rates of change.
Angela’s monthly cost is represented by y = 0.15x + 49.
At 200 minutes, Angela will pay 0.15(200) + 49 or $79.
b. If you ride each train for 5 hours, how far will you travel on each?
The rate of change for Benjamin’s bill is $0.10 per minute.
So, Angela pays more per minute than Benjamin.
Use the graph to find Benjamin's cost. At 200 minutes,
Benjamin will pay $80.
The function for Angela’s bill has a y-intercept of 49. You can see from the graph that the
function for Benjamin’s bill has a y-intercept of 60. So, Benjamin has a greater initial cost.

12. Answer
Need Another Example?
The total cost c to rent any number of
movies m from an online movie rental
company is represented by the function
c = 1.5m + 5. The cost to rent movies
from a different online rental company is
shown in the graph.
a.
b.
Compare the y-intercepts and rates of change.
What will be the cost from each company
if 15 movies are rented in one month?
The function for the first company has a y-intercept of 5
and a rate of change of 1.5. The function for the second
company has a y-intercept of 4 and a rate of change of
2. The y-intercept for the first company is greater than
the y-intercept for the second company but the rate of
change for the first company is less than the rate of
change for the second company.
first company: $27.50; second company: $34

13. 1
Need Another Example?
2
3
4
Step-by-Step Example
4. Financial Literacy Lorena’s mother
needs to rent a truck to move some
furniture. The cost to rent a truck
from two different companies is
shown in the table and graph.
Which company should she use
to rent the truck for 40 miles?
After 40 miles, the cost will be $75 + $25 or $100.
Find the cost of renting a truck from
Ron’s Rentals by extending the table.
The equation y = 0.5x + 30 where y represents the total cost and x represents
the miles driven can be used to find the total cost of renting the truck. After 40
miles, the cost will be 0.5(40) + 30 or $50. So, Cross Town Movers would cost
less for 40 miles.
10 25
20 50
30 75
The slope or rate of change is or 0.5.
Find the cost of renting a truck from Cross Town Movers by
analyzing the graph. The y-intercept of the graph is 30.

14. Answer
Need Another Example?
The eighth grade class is selling pizzas and
subs for a fundraiser. The amount of money they
earn selling pizzas is shown in the table below.
The amount of money they earn selling sub
sandwiches can be represented by the function
m = 4s, where m is the total amount of money
earned and s is the number of sub sandwiches
sold. Which food will the students earn more
money selling if they sell 100 of each item?
pizzas; The students will receive 4(100) or $400
for selling 100 subs, but will earn $500 for selling
100 pizzas.

15. How did what you learned
today help you answer the
HOW can we model relationships
between quantities?
Course 3, Lesson 4-5
Functions

16. How did what you learned
today help you answer the
HOW can we model relationships
between quantities?
Course 3, Lesson 4-5
Functions
Sample answers:
• Functions that are represented in different ways (table,
graph, equation, or words) can be compared.
• You can find the slopes of the different functions to
compare their rates of change.
• You can find the y-intercepts of different functions to
compare their initial values.

17. Create a table of data that
has a constant rate of change.
Find another table of data in
your book. Then compare your
function with the one in the
book by comparing their rates
of change.
Ratios and Proportional RelationshipsFunctions
Course 3, Lesson 4-5