3-4 Functions
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
3-4 Functions
Warm Up
What three terms come next?
1. 9, 12, 15, 18, . . .
21, 24, 27
2. –8, –3, 2, 7, …
12, 17, 22
3. 9, 10, 12, 15, 19, … 24, 30, 37
3-4 Functions
Learn to represent functions with tables,
graphs, or equations.
3-4 Functions
Vocabulary
relation
domain
range
function
independent variable
dependent variable
vertical line test
3-4 Functions
A set of ordered pairs is a relation. The
domain of a relation is the set of x-values
of the ordered pairs. The range of a
relation is the set of y-values of the
ordered pairs.
A function is a special type of relation
that pairs each input, or domain value,
with exactly one output, or range value.
3-4 Functions
Some functions can be written as
equations in two variables. The
independent variable represents the
input of a function. The dependent
variable represents the ouput of a
function.
3-4 Functions
3-4 Functions
3-4 Functions
Additional Example 1: Finding Different
Representations of a Function
Make a table and a graph of y = 3 – x2.
Make a table of inputs and outputs. Use the table to
make a graph.
x
3 – x2
y
–2
3 – (–2)2
–1
–1
3 – (–1)2
2
0
3 – (0)2
3
1
3 – (1)2
2
2
3 – (2)2
–1
3-4 Functions
Check It Out: Example 1
Make a table and a graph of y = x + 1.
Make a table of inputs and outputs. Use the table to
make a graph.
y
x
–1
0
1
2
x+1
y
–1 + 1
0
0+1
1+1
2+1
1
2
3
3
x
–3
2
3-4 Functions
Because a function has exactly one
output for each input, you can use the
vertical line test to test whether a
graph is a function. If no vertical line
intersects the graph at more than one
point, then the relation is a function. If
any vertical line intersects the graph at
more than one point, the the relation
is not a function.
3-4 Functions
Additional Example 2B: Identifying Functions
Determine if the relationship represents a
function.
The input x = 0 has two
outputs, y = 2 and y = –2.
Other x-values also have
more than one y-value.
The relationship is not a
function.
3-4 Functions
Additional Example 2A: Identifying Functions
Determine if the relationship represents a
function.
x
y
2
3
3
4
3
5
2
6
The input x = 2 has two outputs, y = 3 and y = 6.
The input x = 3 also has more than one output.
The relationship is not a function.
3-4 Functions
Check It Out: Example 2A
Determine if the relationship represents a
function.
x
y
0
0
1
1
2
2
3
3
Each input x has only one output y.
The relationship is a function.
3-4 Functions
Check It Out: Example 2B
Determine if the relationship represents a
function.
y
2
x
-2
Since the relationship is
linear there can only be one
output y for each input x.
2
-2
The relationship is a
function.
3-4 Functions
Check It Out: Example 2C
Determine if the relationship represents a
function.
y=x–1
x
x–1
y
0
0–1
–1
1
1–1
0
2
2–1
1
3
3–1
2
Each input x has only one output y.
The relationship is a function.
3-4 Functions
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
3-4 Functions
Lesson Quiz: Part I
1. Graph the function y = x2 – 3.
3-4 Functions
Lesson Quiz: Part II
Determine if each relationship represents a
function.
2.
no
3. y = 3x + 5
yes
3-4 Functions
Lesson Quiz for Student Response Systems
1. Identify the graph of the function
y = x2 – 4.
A.
C.
B.
D.
3-4 Functions
Lesson Quiz for Student Response Systems
2. Identify the relationship that represents a
function.
A.
C.
B.
D.
3-4 Functions
Lesson Quiz for Student Response Systems
3. Identify the relationship that represents a
function.
A. y2 = 4
B. y = 2x
C. y2 = 9
D. y2 = 16