Name:________________________________________________________________________________Date:_____/_____/__________
Spiral Back:
Let’s see what
you
remember!
Evaluate:
1)
Decimal:
Decimal:
Percent:
10-3
Fraction:
2)
Fraction:
3
8
Scientific Notation
Standard Form
3)
4)
82,500,000
3.4 x 10-4
x = -2 and y = 3
Evaluate the following when
5)
xy + (y – x)2
Solve the following equations:
6)
x – 4 = -12
7)
2x – 2 = -16
8)
x
6
+ 4 = 10
Today’s Lesson:
What:
Identifying a function
Why:
To identify a function and become
familiar with basic function vocabulary.
Input
Output
What to expect in this unit . . .
Up to now, you have solved equations
with only one variable. In this unit, you
will see a type of equation that has
variables– an
!! You
will learn that these equations graph as a
straight line.
When you hear things like x . . . y . . .
and graph . . . Does anything come to
mind?? Think about what you learned in
6th grade. What do you think??
COORDINATE PLANE
SOUND FAMILIAR??
In this unit, we will be
graphing linear equations
on a coordinate plane. Let’s
see what you remember
about plotting points!!!
Coordinate plane review:
Label the following parts:
origin x axis y axis Quad Quad Quad Quad
I
II
III
IV
y
Q II
QI
F
A
E
x
B
G
C
Q III
D
Q IV
On the above coordinate plane, plot the following
points:
A
B
C
D
E
F
G
(2, 3) (-3,-1) (0, -6) (9, -5) (-6, 0) (-4, 6) (4, -4)
Essential vocabulary:
Ordered Pair
A name we use for the x and
_______
y values that make up a
point on the coordinate
plane.
Relation
A group of ordered
_____________________.
pairs
Function
A special ___________________
of
TYPE
relation where there is one
and only one “y” value for
every “x” value. (“x” can
never repeat)
All functions are relations, but
Not all relations are functions!!!
Essential vocabulary:
3 ways to name “x” and “y”:
x
INPUT
y
OUTPUT
DOMAIN
INDEPENDENT
RANGE
DEPENDENT
What is the Domain of the
following relation?
{(1,2); (2,3); (3, 4); (4,5)}
D = {1, 2, 3, 4}
_____________________________________
What is the Range of the
following relation?
{(1,3); (2,5); (3, 7); (4,9)}
R = {3, 5, 7, 9}
______________________________________
4 ways to represent a function:
1
As an
equation
2
3
“y is equal to the
product of 4 and
x, minus two.”
With
___________
WORDS
As a
table
4
y = _______
4x - 2
As a
_________
GRAPH
See? An
equation
with BOTH
x and y!!
x
0
1
2
3
y
-2
2
6
___
10
How to identify a function . . .
METHOD ONE: Look to see if the “x” values
x value
repeat . . . If there is more than one _______
NOT a
that is the same #, then the relation is ___________
function!
Are the following examples functions? Answer
“YES” or “NO”
YES
1) ___________
YES
2) _____________
NO
3) ______________
x
0
1
2
y
3
3
3
x y
-5 0
0 5
5 10
x y
-1 -2
0 0
-1 -4
3
3
10 15
1
2
YES
4) __________
{ (-2, 0); (0, 2); (2, 0); (4, 6) }
NO
5) __________
{ (-2, 0); (0, 3); (-2, 2 ); (5, 7) }
METHOD TWO: VERTICAL LINE TEST—
Look at the graph of the function. If any two points
vertical
on the graph can be connected by a ________________
line, then the relation is NOT a function!
Are the following examples functions? Answer
“YES” or “NO”
YES
NO
1) __________
2) __________
YES
4) __________
3) __________
NO
homework
IXL:
Q.4 & Q.5
,
END OF LESSON
The next slides are student copies of the notes and/or
handouts for this lesson. These were handed out in
class and filled-in as the lesson progressed.
NAME:
DATE: ______/_______/_______
Math-7 NOTES
What: identifying a function
Why:
To identify a function and become familiar with basic function vocabulary.
Coordinate plane review:
Label the following parts:
origin
x axis
y axis
Quadrant
I
Quadrant
II
Quadrant
III
Quadrant
IV
F(-4, 6)
G(4, -4)
On the above coordinate plane, plot the following points:
A(2, 3)
B(-3, -1)
C(0, -6)
D(9, -5)
E(-6, 0)
Essential vocabulary:
Ordered Pair
A name we use for the
x and _____ values that
make up a point on the
coordinate plane.
Relation
A group of ordered
__________________.
All functions are relations, but
Not all relations are functions!!!
Function
A special _______________ of
relation where there is
one and only one “y”
value for every “x” value.
(“x” can never repeat)
3 ways to name x and y . . .
x
y
What is the Domain of the
following relation?
{(1,2); (2,3); (3, 4); (4,5)}
_________________________________
RANGE
What is the Range of the
following relation?
{(1,3); (2,5); (3, 7); (4,9)}
_________________________________
INPUT
INDEPENDENT
4 ways to represent a function:
1
As an
equation
y = _______
2
“y is equal to the
product of 4 and x,
minus two.”
With
___________
3
As a table
x
y
0
-2
1
2
2
6
3
_____
4
As a _______
How to identify a function . . .
METHOD ONE: Look to see if the “x” values repeat . . . If there is more than one
_______ value that is the same #, then the relation is ______ a function!
Are the following examples functions? Answer “YES” or “NO”
1) ____________
2) _______________
3) _______________
x
y
x
y
x
y
0
3
-5
0
-1
-2
1
3
0
5
0
0
2
3
5
10
-1
-4
3
3
10
15
1
2
4) __________
{ (-2, 0); (0, 2); (2, 0); (4, 6) }
5) __________
{ (-2, 0); (0, 3); (-2, 2 ); (5, 7) }
METHOD TWO: VERTICAL LINE TEST—Look at the graph of the function.
If any two points on the graph can be connected by a ________________ line, then the
relation is NOT a function!
Are the following examples functions? Answer “YES” or “NO”
1) __________
2) __________
3) __________
4) __________
IXL: ALGEBRA 1, Q.4 & Q.5
NAME:_________________________________________________________________________________ DATE:_____/_____/__________
Math-7 Exit ticket
1) On the below coordinate plane, plot the following points (label each pt. with its letter):
A(6, 2)
B(-4, 6)
C(0, -2)
D(-2, -5)
E(8, -3)
F(-9, 0)
G(-3, -4)
2) We have 3 ways to name both the “x” variable and the “y” variable. Fill in the missing
information with the appropriate vocabulary:
x
y
Output
3) What is the Domain of the following relation?
{(0,3); (-5,5); (-2, 7); (8,9)}
D = _________________________________
4) What is the Range of the following relation?
{(1,-2); (2,0); (3, 2); (4,4)}
R= _________________________________
5) A __________________________________ is a group of ordered pairs. A ________________________________ is a
special type of relation where all the “x” values match with one and only one “y” value. (the “x”
can never repeat).
6) What are the 4 ways to represent a function (from our notes)?
NAME:_________________________________________________________________________________ DATE:_____/_____/__________
Math-7 PRACTICE
NAME:_________________________________________________________________________________ DATE:_____/_____/__________
Math-7 PRACTICE