Transcript PC_functions_ CC

P.O. I can compare two functions represented
in different ways.
L.O. I can define relation and function. I can
determine whether a relation represented in
different ways is a function.
E.Q. What is a function? How do you identify
a function? What are some ways in which you
can represent functions?
Motivate
You and your friends are going to a basketball
game. What is the relation between the total cost
for tickets and the number of people in your group?
Total cost is equal to the individual
ticket price multiplied by the number
of people in the group.
Vocabulary:
Relation A set of ordered pairs represented as
(x,y).
(0,3); (6,5); (3,7)
The set of x-coordinates of the ordered
Domain
pairs.
0, 6, 3
Range
The set of y-coordinates.
3, 5, 7
Find the domain and range from the table below
$ of order
(x)
$10 $12
$16
$18
$27
$ including
shipping (y)
$14 $16
$20
$22
$31
• What is another name for
Domain and Range?
Vocabulary:
Function A relation in which no two ordered pairs
have the same x-coordinate.
Example
This relation is a function:
(0,10), (1,2), (2,3)
This relation is not a function:
(1,1), (1,2), (2,3)
What is a Function???
Examples
Non Examples
(3,90), (4,54), (6,71)
(13,14), (13,5) , (16,7)
(3,4), (4,5), (6,7), (3,9)
(-1,2), (-4,51), (1,2)
(8, 11), (34,5), (6,17), (8,19)
(3,4), (4,5), (6,7), (1, 2)
What is a Function???
Examples
Non Examples
(3,90), (4,54), (6,71) (13,14), (13,5) , (16,7)
(-1,2), (-4,51), (1,2)
(3,4), (4,5), (6,7), (3,9)
(3,4), (4,5), (6,7), (1,
(8, 11), (34,5), (6,17), (8,19)
2)
Guided practice
Is this a function? Explain your answer.
1. (6,1), (4,2), (6,-3),(2,5)
2. (5,8), (3,-2), (-2,-5),(0,0)
3. (2,4), (2,5), (2,6),(2,7)
Representations of functions....
1. ordered pairs- (1,0), (2,0), (3,3)
2. contextual situations
3. inputs and outputs-
4. graphs5. Equations
Create a mapping from the set of
ordered pairs. Is it a function?
a) (5,8), (11,9), (6,8), (8,5)
b) (3,4), (9,8), (3,7), (4,20)
Input and Outputs
Input output
x
y
-10
20
20 -10
-5
10
10
-5
0
0
0
0
5
10
10
5
10
20
20
10
State the domain and the range for each relation. Then
determine which relations represent functions. If the
relation is not a function, state why not.
Think
Is it easier to determine if a relation is a function by
viewing a mapping, a set of ordered pairs, or a table?
Analyzing Contexts
Example: Read each context and decide
whether it fits the definition of a function. Explain your
reasoning.
1. a) Input: Sue writes a thank-you note to her
best friend.
b) Output: Her best friend receives the thankyou note in the mail.
2. a) Input: A football game is being telecast.
b) Output: It appears on televisions in
millions
of homes.
Read each context and decide whether it fits the
definition of a function. Explain your reasoning.
1. a) Input: The basketball team has numbered
uniforms.
b) Output: Each player wears a uniform with her
assigned number.
2. a) Input: Tim sends a text message to everyone
in her contact list.
b) Output: There are 41 friends and family on
Tim’s contact list.
3. a) Input: A sneak preview of a new movie is
being shown in a local theater.
b) Output: 65 people are in the audience
Did you know?
Functions can also be represented using an
equation!!!
Analyzing equations
y = 3x
To test whether this equation is a function,
first substitute values for x into the
equation, and then determine if any xvalue can be mapped to more than one yvalue.
Guided Practice
Determine whether each equation is a function.
List three ordered pairs that are solutions to
each. Explain your reasoning.
a) y = 5x+ 3
b) y = x2
c) y = x
Vertical line test
You can determine whether a graph
represents a function by using the vertical line
test. If any vertical line intersects a graph at
more than one point, the graph does not
represent a function. Otherwise, the graph
does represent a function.
Not a function!
Think and Discuss
Does the graph above represent a function? Explain
Think and Discuss
Does the graph above represent a function? Explain
Think and Discuss
• Is this a linear function or a nonlinear function?
Ticket out
• A relation is (always, sometimes, never)
a function.
• A function is (always, never) a relation
Homework
1. Create a mapping that is a function.
2. Draw a graph that is not a function
3. Create a table that is a function
4. Create your own context problem, and
decide whether it represents a function.