(8) Lesson 4.3

1. Course 3, Lesson 4-3
1. At a water park, you can rent a raft for $2 per hour.
a. Make a table of ordered pairs in which the x-coordinate
represents the number of hours and the y-coordinate
represents the total cost for 1, 2, 3, or 4 hours.
b. Graph the ordered pairs.
2. State the domain and range of the relation.
{(3, 6), (-1, 0), (2, 6), (-4, -5)}
3. What is the range of the relation {(4, 1), (0, 2), (3, 3), (6,1)}?

2. Course 3, Lesson 4-3
ANSWERS
1a. 1b.
2. Domain: {-4, -1, 2, 3};
Range: {-5, 0, 6}
3. {1, 2, 3}

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

4. Course 3, Lesson 4-3 4-1 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.1
Understand that a function is a rule that assigns to each input exactly
one output. The graph of a function is the set of ordered pairs
consisting of an input and the corresponding output.
• 8.F.4
Construct a function to model a 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 4-3 4-1 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
• find the value of a function for a
certain number,
• make a function table of values
Course 3, Lesson 4-3
Functions

7. • function
• function table
• independent variable
• dependent variable
Course 3, Lesson 4-3
Functions

8. 1
Need Another Example?
2
3
4
Step-by-Step Example
1. Find f(–3) if f(x) = 2x + 1.
f(x) = 2x + 1 Write the function.
f(–3) = 2(–3) + 1 Substitute –3 for x into the function rule.
f(–3) = –6 + 1 or –5 Simplify.
So, f(–3) = –5.

9. Answer
Need Another Example?
Find f(–6) if f(x) = 3x + 4.
–14

10. 1
Need Another Example?
2
3
Step-by-Step Example
2. Choose four values for x to make a function table
for f(x) = x + 5. Then state the domain and range of
the function.
Substitute each domain value x into the function rule.
Then simplify to find the range value.
The domain is {–2, –1, 0, 1}.
The range is {3, 4, 5, 6}.

11. Answer
Need Another Example?
Choose four values for x to make a function
table for f(x) = 4x – 1. Then state the domain
and range of the function.
D: {−2, −1, 0, 1}; R: {−9, −5, −1, 3}

12. 1
Need Another Example?
Step-by-Step Example
3. There are approximately 770 peanuts in a jar of peanut
butter. The total number of peanuts p(j) is a function of
the number of jars of peanut butter j.
Since the total number of peanuts depends on the number
of jars of peanut butter, the number of peanuts p(j) is the
dependent variable and the jars of peanut butter j is the
independent variable.
Identify the independent and dependent variables.

13. Answer
Need Another Example?
Linda buys a can of tuna fish that weighs
4.2 ounces. The total weight w(c) is a function
of the number of cans of tuna fish c. Identify
the independent and dependent variables.
The number of cans c is the independent
variable. The total weight w is the dependent
variable.

14. 1
Need Another Example?
Step-by-Step Example
4. There are approximately 770 peanuts in a jar of peanut
butter. The total number of peanuts p(j) is a function of
the number of jars of peanut butter j.
Only whole numbers make sense for the domain because
you cannot buy a fraction of a jar. The range values depend
on the domain values, so the range will be multiples of 770.
What values of the domain and range make sense for
this situation? Explain.

15. Answer
Need Another Example?
Linda buys a can of tuna fish that weighs
4.2 ounces. The total weight w(c) is a function
of the number of cans of tuna fish c. Explain
what values of the domain and range make
sense for this situation.
Only whole numbers make sense for the
domain because you cannot buy a fraction
of a can of tuna fish. The range will be
multiples of 4.2.

16. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
5. There are approximately 770 peanuts in a jar of peanut butter.
The total number of peanuts p(j) is a function of the number
of jars of peanut butter j.
The function p(j) = 770j represents the situation.
Write a function to represent the total number of peanuts. Then
determine the number of peanuts in 7 jars of peanut butter.
Words The number
of peanuts equals
770
times
the number
of jars
p(j) = 770 • jFunction
To find the number of peanuts in 7 jars of peanut butter,
substitute 7 for j.
p(j) = 770j Write the function.
p(j) = 770(7) or 5,390 Substitute 7 for j.
There are 5,390 peanuts in 7 jars of peanut butter.

17. Answer
Need Another Example?
Linda buys a can of tuna fish that weighs 4.2
ounces. The total weight w(c) is a function of the
number of cans of tuna fish c. Write a function to
represent the total weight. Then determine the
ounces in 8 cans of tuna fish.
w(c) = 4.2c; 33.6 oz

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

19. How did what you learned
today help you answer the
HOW can we model relationships
between quantities?
Course 3, Lesson 4-3
Functions
Sample answers:
• A special type of relation is a function.
• In a function, every member of the domain is paired
with exactly one member of the range.
• Functions can be modeled by function tables and
function rules.

20. Explain how to find a
function value given a rule
and value in the domain.
Substitute the value in the
function and evaluate.
Ratios and Proportional RelationshipsFunctions
Course 3, Lesson 4-3