Formalizing Relations
and Functions
Objectives:
To determine whether a relation is
a function
To find domain and range and use
function notation
Relation:
a pairing of numbers in one set with
numbers in another set
Domain:
the set of x-values
Range:
the set of y-values
Problem #1: Identifying Functions
Using Mapping Diagram
Identify the domain and range of the relation.
Represent the relation with a mapping diagram. Is
the relation a function?
A)
{(-2, 0.5), (0, 2.5), (4, 6.5), (5, 2.5)}
Problem #1: Identifying Functions
Using Mapping Diagram
Identify the domain and range of the relation.
Represent the relation with a mapping diagram. Is
the relation a function?
B)
{(6,5), (4,3), (6,4), (5,8)}
Problem #1
Got It?
Identify the domain and range of each relation.
Represent the relation with a mapping diagram. Is
the relation a function?
Vertical Line Test
Another method used to determine if a
relation is a function.
Look at the graph and determine if any
vertical line passes through more than
one point of the graph, then the relation
is not a function.
Problem #2: Identifying Functions
Using the Vertical Line Test
Is the relation a function? Use the Vertical
Line Test.
A) {(-4, 2), (-3, 1), (0,-2), (-4, -1), (1, 2)}
Problem #2: Identifying Functions
Using the Vertical Line Test
Is the relation a function? Use the Vertical
Line Test.
B) 𝑦 = −𝑥 2 + 3
Problem #2
Got It?
Is the relation a function? Use the Vertical
Line Test.
Function Notation
y = -3x + 1 is the same as 𝑓 𝑥 = −3𝑥 + 1
-
f(x) replaces y
read “f of x”
f is the name of the function, not a variable
Used to emphasize that the function value
f(x) depends on the independent variable x.
- Other letters besides f can also be used, such
as g and h.
Problem #3: Evaluating a Function
A) The function w(x) = 250x represents
the number of words w(x) you can read in
x minutes. How many words can you read
in 8 minutes?
Problem #3: Evaluating a Function
B) The function Y(x) =
1
𝑥
3
represents the
number of yards Y(x) in x feet. How
many yards are there in 1 mile?
Problem #3
Got It?
The function T(x) = 65x represents the
number of words T(x) that Rachel can
type in x minutes. How many words can
she type in 7 minutes?
*Homework
Textbook Page 271; #1 – 3, 5 – 17 All
Continued…
Objectives:
To determine whether a relation is
a function
To find domain and range and use
function notation
Problem #4: Finding the Range of a
Function
A) Multiple Choice
The domain of f(x) = 1.5x + 4 is {1, 2, 3, 4}.
What is the range?
Problem #4: Finding the Range of a
Function
B)
The domain of g(x) = 4x – 12 is {1, 3, 5, 7}.
What is the range?
Problem #4
Got It?
What is the range of f(x) = 3x – 2 with
domain {1, 2, 3, 4}?
Problem #5: Identifying a Reasonable
Domain and Range
A) You have 3 qt. of paint to paint the
trim in your house. A quart of paint covers
100 𝑓𝑡 2 . The function 𝐴(𝑞) =
100𝑞 represents the area A(q), in square
feet, that q quarts of paint cover. What
domain and range are reasonable for the
function? What is the graph of the
function?
Problem #5: Identifying a Reasonable
Domain and Range
B) Lorena has 4 rolls of ribbon to make
party favors. Each roll can be used to
make 30 favors. The function F(r) = 30r
represents the number of favors F(r) that
can be made with r rolls. What are a
reasonable domain and range of the
function? What is a graph of the function?
Problem #5
Got It?
A car can travel 32 miles for each gallon of
gasoline. The function d(x) = 32x
represents the distance d(x), in miles, that
the car can travel with x gallons of
gasoline. The car’s fuel tank holds 17 gal.
Find a reasonable domain and range for
each function. Then graph the function.
*Homework
4 – 6 Worksheet