# Functions by ferda.gurcan

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```									 3-4 Functions
3-4 Functions

Warm Up
Problem of the Day
Lesson Presentation

Course
Course 33
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

Course 3
3-4 Functions

Problem of the Day
Sandra, Greg, and Michael team up for
a competitive eating contest. If Sandra
can eat 3 hot dogs per minute, Greg
can eat 4 hot dogs per minute, and
Michael can eat 5 1 hot dogs per minute,
2
how long will it take them to
eat a combined total of 100 hot dogs?
8 minutes

Course 3
3-4 Functions

Learn to represent functions with tables,
graphs, or equations.

Course 3
3-4 Functions

Vocabulary
function
input
output
domain
range
vertical line test

Course 3
3-4 Functions

A function is a rule that relates two
quantities so that each input value
corresponds to exactly one output
value.
The domain is the set of all possible
input values, and the range is the set
of all possible output values.

Course 3
3-4 Functions

Functions can be represented in many
ways, including tables, graphs, and
equations. If the domain of a function
has infinitely many values, it is
impossible to represent them all in a
table, but a table can be used to show
some of the values and to help in
creating a graph.

Course 3
3-4 Functions
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

Course 3
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    x+1      y
3
–1      –1 + 1    0
0    0+1      1                            x
–3           2
1    1+1      2
2    2+1      3

Course 3
3-4 Functions

If a relationship is a function, each
input has exactly one output. When the
relationship is graphed, use the
vertical line test. Place a vertical line
on the graph. If the line intersects the
graph at only one point, then the
relationship is a function. If the line
intersects the graph at more than one
point, then the relationship is not a
function.

Course 3
3-4 Functions

11
Course 3
3-4 Functions

Determine if the relationship represents a
function.

x   y   The input x = 2 has two outputs, y
2   3   = 3 and y = 6. The input x = 3
also has more than one output.
3   4
3   5   The relationship is not a function.
2   6

Course 3
3-4 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.

Course 3
3-4 Functions
Determine if the relationship represents a
function.
y = x3
Make an input-output table and use it to graph y = x3.
x          y
–2      (–2)3 = –8
–1      (–1)3 = –1
0    (0)3 = 0
1    (1)3 = 1
2       (2)3 = 8
Each input x has only one output y.
The relationship is a function.
Course 3
3-4 Functions
Check It Out: Example 2A

Determine if the relationship represents a
function.

x   y
Each input x has only one output
0   0      y.
1   1
The relationship is a function.
2   2
3   3

Course 3
3-4 Functions
Check It Out: Example 2B

Determine if the relationship represents a
function.
y

Since the relationship is
2                linear there can only be one
x   output y for each input x.
-2            2

-2               The relationship is a function.

Course 3
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.
Course 3
3-4 Functions
Lesson Quiz: Part I

1. Graph the function y = x2 – 3.
y

4

2

x
-4   -2            2   4

-2

-4

Course 3
3-4 Functions
Lesson Quiz: Part II

Determine if each relationship represents a
function.
2.

no

3. y = 3x + 5

yes

Course 3

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