Download Frayer Model - Tapp Middle School

December 10, 2010
Functions and Relations
Warm Up
1. Evaluate
2
3 3
2. Solve:
3. Solve:
7  3  3  2
3
 3 x  7  14
x  8 - 5 = -4
3
Frayer Model
Examples
Definition
Linear
Relation
Non-Linear
Frayer Model
Examples
Definition
A set containing pairs of
numbers
Linear
Relation
Non-Linear
Frayer Model
Examples
Definition
{(2,1), (1,3), (0,4)}
A set containing pairs of
numbers
Linear
2
1
0
Relation
1
3
4
x
2
1
0
y
1
3
4
Non-Linear
Frayer Model
Examples
Definition
{(2,1), (1,3), (0,4)}
A set containing pairs of
numbers
Linear
2
1
0
Relation
1
3
4
x
2
1
0
y
1
3
4
Non-Linear
Frayer Model
Examples
Definition
{(2,1), (1,3), (0,4)}
A set containing pairs of
numbers
Linear
2
1
0
Relation
1
3
4
x
2
1
0
y
1
3
4
Non-Linear
Frayer Model
Examples
Definition
a relation in which each
input (x value) is paired with
exactly one output (y value).
Linear
Function
Non-Linear
Frayer Model
Examples
Definition
a relation in which each
input (x value) is paired with
exactly one output (y value).
Linear
{(1,2), (2,4), (3,6)}
1
2
3
Function
2
4
6
x
1
2
3
y
2
4
6
Non-Linear
Frayer Model
Examples
Definition
a relation in which each
input (x value) is paired with
exactly one output (y value).
Linear
{(1,2), (2,4), (3,6)}
1
2
3
Function
2
4
6
x
1
2
3
y
2
4
6
Non-Linear
Frayer Model
Examples
Definition
a relation in which each
input (x value) is paired with
exactly one output (y value).
Linear
{(1,2), (2,4), (3,6)}
1
2
3
Function
2
4
6
x
1
2
3
y
2
4
6
Non-Linear
Is this relation a function?
{(1,3), (2,3), (3,3)}
1. Yes
2. No
Answer Now
Are these relations functions?
1. (1, 2), (3, 4), (1, 5), (2, 6)
2. (6, 9), (7, 10), (8, 11), (8, –11)
3. (–1, –5), (–2, –7), (0, 3), (1, –5)
4. (2, 4), (3, 5), (2, -4), (3, –5)
Are these relations functions?
1.
2.
3.
x
1
2
3
4
y
5
6
6
7
x
2
4
5
5
Y
1
2
3
4
x
6
5
4
3
Y
-1
-2
-3
-4
Are these relations functions?
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
Vertical Line Test (pencil
test)
If any vertical line passes through
more than one point of the graph,
then that relation is not a function.
Are these functions?
FUNCTION!
FUNCTION!
NOPE!
Vertical Line Test
FUNCTION!
NO!
NO WAY!
FUNCTION!
Is this a graph of a function?
1. Yes
2. No
Answer Now
An Equation is not a Function if…
1. the “y” variable is raised to an EVEN
power; y 2 or y 6
2. x = any number; x = 5 and x = -9 – these
are vertical lines.
Are these functions?
•
•
•
•
•
•
y=x2
x+y4=5
y=x+3
y+6=x3
x=3
y3=x2+4
•
•
•
•
•
•
Yes
No, y is raised to an even power!
Yes
Yes
No, because the line is vertical!
Yes
An Equation is NOT linear if…
1. any two variables are being multiplied
together, Or…
2. there is a power on any variable greater
than 1,
Or…
3. there is a variable in the denominator.
Is the following equation linear?
• 2a + 3b = 4
• Are any two variables
being multiplied together?
• Is there a power on any
variable greater than 1?
• Is there a variable in the
denominator?
• Since the answer to all of
the questions is “no,” the
equation is linear.
No!
No!
No!
Is the following equation linear?
• y = 5x – 3xy
• Are any two variables
being multiplied together?
• Is there a power on any
variable greater than 1?
• Is there a variable in the
denominator?
• Since the answer to the
first question is “yes,” the
equation is nonlinear.
Yes!
No!
No!
Is the following equation linear?
1
• y=
x
• Are any two variables
being multiplied together?
• Is there a power on any
variable greater than 1?
• Is there a variable in the
denominator?
• Since the answer to the
third questions is “yes,”
the equation is nonlinear.
• No!
• No!
• Yes!
Is the following equation linear?
• A=s2
• Are any two variables
being multiplied together?
• Is there a power on any
variable greater than 1?
• Is there a variable in the
denominator?
• Since the answer to the
second questions is
“yes,” the equation is
nonlinear.
• No!
• Yes!
• No!
Is the table linear?
x
1
2
3
4
y
3
6
9
12
3
3
3
Yes! The “x” values increase by 1 and the “y”
differences are the same. Therefore, this
relationship is linear.
Is the table linear?
x
4
5
6
7
y
16
25
36
49
9
11
13
No! Though the “x” values increase by 1, the
“y” differences are not the same. Therefore,
this relationship is nonlinear.