Name:________________________________________________________________________________Date:_____/_____/__________
Fill-in-the-Blanks:
1) A relation is a _______________ of ordered pairs.
2) A ________________________ is a special type of relation, where
every x value has one and only one y value (the relationship
between x and y remains consistent).
3) In a function, the x value can never ___________________ .
4) Fill-in-the-table:
x
y
Input
Domain
Dependent
5) What is the domain of the following relation?
{ (-2, 4); (0, 8); (2, 12); (4, 16) }
D = ____________________________________________
Are the following relations functions? Answer “yes” or “no” :
6) _____
x
y
-8
7)_____
x
y
4
-2
-4
4
0
4
8)_____
x
y
2
-4
2
0
0
0
0
4
2
2
4
-2
4
4
4
0
-4
9) _____ {(-1, 5); (0, 5); (1, 5); (2, 5)}
10)_____ {(3, 7); (5, 11); (7, 15); (3, 10)}
Plot each point in order, connecting the points with a line . Tip:
Make the line as you plot the points– don’t wait until the end.
11)
12) What are the four ways to represent a function?
1. Equation 2._________ 3._________ 4.________
(y = 2x + 5)
Today’s Lesson:
What:
Function tables
Why:
Given a function table, to represent said
table as an equation and as a graph.
Input
Output
Consider the following pattern:
1
2
3
1) The above represents a toothpick pattern. How
12
many toothpicks would be in Figure #4? ________
2) Fill-in-the-table:
We can say that
the # of
Toothpicks is a
function of the
Figure #. “y”
depends on “x.”
Figure #
(x)
# of
Toothpicks
(y)
1
3
2
6
9
12
15
18
3
4
5
6
3) Is there an easy way to see how many toothpicks
Yes !
we would need for Figure #100?
There is a “times 3” rule going from x to y, so we would
need 300 toothpicks!
4) Let’s write this “rule” as an equation:_____________
y = 3x
Sometimes it is helpful to think of a
Function table as an input/output
“Machine” . . .
As the inputs (x values) and outputs (y values) are
revealed, can you figure out the “machine rule”?
5)
Input
(x)
Output
(y)
0
1
3
4
2
5
3
4
6
7
Rule: “plus 3”
Equation: y = x + 3
50
53
6)
Input
(x)
Output
(y)
1
4
2
7
3
10
4
13
16
5
Rule: “times 3, plus 1”
Equation: y = 3x +1
100
301
7)
Input
(x)
Output
(y)
1
1
2
3
3
5
4
7
9
5
Rule:
“times 2, minus 1”
Equation:
y = 2x - 1
40
79
Every input/output is an ordered pair,
so it is easy to graph . . .
Notice the straight line.
We will be studying
linear functions during
this unit. They will ALL
graph as a straight line!
“Toothpick Patterns Lab”
Wait for directions from teacher . . .
We will now continue our regular
lesson, so get your notes back out . . .
Is there a shortcut? Yes . . . I call
it The “magic number” shortcut . . .
Step One: Find the pattern going down the “y”
column. This is the magic number !
(x)
(y)
1
2
3
4
5
4
6
8
There is a
+2
pattern going
down the y
column . . .
10
12
Step Two: The magic number tells you what to
multiply x by! Our magic # is __________
.
2
So, the first part of the equation is 2x . . .
Step Three: See if you need a second step . . .
When we multiply our “x” numbers by 2, we see
that we still need to add 2 in order to equal “y.”
Final Equation:
y = 2x + 2
Catch– the “magic”
only works if your
inputs are in a row!!
Let’s tie it all together (use the shortcut to
help You) . . .
8)
Table:
Graph:
(x)
(y)
0
-2
1
1
2
4
3
7
4
10
Equation:
y = 3x - 2
+ 3 pattern . . .
This is a subtraction pattern going down
“y.” This means the magic # is negative!
9)
Table:
(x)
(y)
0
0
1
-2
2
-4
3
-6
-8
4
Graph:
Equation:
y = -2x
- 2 pattern . . .
Your turn . . .
10)
Table:
Graph:
(x)
(y)
2
-4
3
-1
4
2
5
5
6
8
Equation:
y = 3x - 10
+3 pattern . . .
11)
Table:
This is a subtraction pattern going down
“y.” This means the magic # is negative!
(x)
(y)
-3
10
-2
6
-1
2
0
-2
-6
1
Equation:
y = -4x - 2
- 4 pattern . . .
Graph:
Your turn . . .
Your turn . . .
12)
Table:
(x)
(y)
3
6
4
7
5
8
6
9
10
7
Equation:
y= x+3
+1 pattern . . .
Graph:
When the pattern going down “y” is “plus 1,” it means that the
equation does not need a multiplication step.
homework
IXL: 7th Grade
V.6 & V.10
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: Function tables
Why: Given a function table, to represent said table as an equation and as a graph.
Consider the following pattern:
1
2
3
1) The above represents a toothpick pattern. How many toothpicks would be in
Figure #4??_________
2) Fill-in-the-table:
Figure #
(x)
# of
Toothpicks (y)
1
3
3) Is there an easy way to see how many toothpicks we
would need for Figure #100?
2
4)
3
Let’s write this “rule” as an equation: _______________
4
5
6
Sometimes it is helpful to think of a Function table as an put/output
“Machine” . . .
As the inputs (x values) and outputs (y values) are revealed, can you figure out the
“machine rule” (fill in numbers as they are revealed)?
5)
Input
(x)
Output
(y)
Rule:
Equation:______________
6)
Input
(x)
Output
(y)
1
4
2
7
3
10
4
Rule:
Equation:______________
5
7)
Input
(x)
Output
(y)
1
1
2
3
3
5
4
Rule:
Equation:______________
5
Every input/output is an ordered pair, so it is easy to graph . . .
Graph for #7 . . .
Time for “toothpick patterns” lab (wait for directions) . . .
Is there a shortcut? Yes . . . I call it The “magic number” shortcut . . .
Step One: Find the pattern going down the “y”column. This is the magic number !
(x)
(y)
1
4
2
6
3
8
There is a
+2
pattern going down
the y column . . .
4
5
Step Two:
The magic # tells you what to multiply x by! Our magic # is __________ .
Step Three: See if you need a second step in order to equal y . . . ________________
Final Equation: __________________________
Let’s tie it all together (use the shortcut to help You) . . .
Table:
8)
(x)
(y)
0
-2
1
1
2
4
Graph:
3
4
Equation:___________________________
9)
Table:
(x)
(y)
0
0
1
-2
2
-4
Graph:
3
4
Equation:___________________________
When there is a subtraction pattern, the “magic number” is negative!!
Find the pattern going down the “y” column. This is
the magic #! Multiply this # to x!!
Your turn . . .
10)
Table:
(x)
(y)
2
-4
3
-1
4
2
Graph:
5
6
Equation:___________________________
This is a subtraction pattern going down “y.”
This means the magic # is negative!
11)
Table:
(x)
(y)
-3
10
-2
6
-1
2
Graph:
0
1
Equation:___________________________
12)
Table:
(x)
(y)
3
6
4
7
5
8
Graph:
6
7
Equation:___________________________
When the pattern going down “y” is “plus 1,” it means that the
equation does not need a multiplication step.
IXL: 7TH Grade, V.6 & V.10
Name:__________________________________________________________________ Date:_____/_____/__________
“Toothpick Patterns Lab”
1) Extend the Toothpick pattern below. How many toothpicks are in Figure # 4 ? _____
1
2
3
4 (draw below)
2) Use the pattern in #1 to complete the below table. List the # of toothpicks in each figure.
Figure #
(x)
# of
Toothpicks (y)
1
2
2
3
4
5
6
3) Is it possible to have a figure with 40 toothpicks? Explain.
4) How many toothpicks would be in Figure # 20?
5) The # of toothpicks increases by 4 each time. This is a “+4” pattern for the (y) column in the
above table. What is the pattern (or rule) for going from (x) to (y)?
6) Use your answer to #5 in order to write the equation for finding the number of toothpicks (y)
given the figure number (x):
y=
NAME:_________________________________________________________________________________DATE: ______/_______/_______
EXIT TICKET
“Toothpick Patterns Lab”
1) In the function table featured in the lab, the “x” column stood for the
Figure #. What did the “y” column stand for?
2) This is the same table from the lab:
Figure #
(x)
# of
Toothpicks (y)
1
2
2
6
3
10
4
14
5
18
6
22
Write the equation here: __________________________________________________
3.
How many toothpicks would be required to build Figure # 100?
Name: _______________________________________________ Date:_____/_____/__________
Math-7 PRACTICE
“Equations from Tables”
Find the pattern going down the “y” column. This is the magic #! Multiply
this # to x!! If it is a subtraction pattern, the magic # is negative!!
Directions: Fill in the missing spaces in the below function tables.
Then, write the equation:
1)
2)
3)
(x)
(y)
(x)
(y)
(x)
(y)
-2
-10
-3
10
0
3
-1
-5
-2
7
1
5
0
0
-1
4
2
7
1
0
4
2
1
5
x
y =_______
(equation)
4)
x
y =_______
(equation)
5)
x
y= _______
(equation)
6)
(x)
(y)
(x)
(y)
(x)
(y)
6
30
-6
0
0
4
7
34
-5
1
1
0
8
38
-3
2
2
-4
9
-2
4
10
-1
5
x
y =_______
(equation)
x
y =_______
(equation)
x
y= _______
(equation)
7) Fill-in-table AND graph:
(x)
(y)
0
2
1
5
2
8
3
4
X
y =_______
(equation)