Transcript Objective – To use tables to represent functions.

Objective – To use tables to represent
functions.
A relation is a function if for each input there is
EXACTLY one output.
Input-Output Table
(Function Table)
Input
(X)
Output
(Y)
0
1
2
3
3
6
9
12
Input and Output can also be written
as an ordered pair.
(X , Y)
(0, 3)
Input
(Input, Output)
(1, 6)
Output
(2, 9)
(3, 12)
Function - A rule or equation where there is
exactly one output for every input. For every
x-value there is exactly one y-value.
x y
x y
x y
-1 -2
-1 2
1 -2
No x- 0 0
No x- 0 0
0 0
x-value
value 1 2
value 1 2
1 2
repeats
repeats
repeats
2 4
2 4
2 4
4 6
4 6
4 6
-2
-1
Yes, it is a
1
2
2
1
function
Yes, it is a
No, it is not
function
a function
Determine whether the relation is a function:
1. (0, 2) (1, 4) (2, 6) (3, 8)
YES
Each input has
exactly one output!!!
Input
9 25 9 25 5
2.
Output 3 -5 -3 5 2
NO
Both 9 and 25 has
two different outputs!
9 25 9 25 5
3 -5 -3 5 2
Determine whether the relation is a function:
3. (-2, 4) (2, 4) (4, 2) (-2, -4)
4. (4, 5) (2, -3) (4, 9) (-2, -3)
NO
NO
5.
Input
(X)
Output
(Y)
-2
3
8
13
0
0
0
0
6.
YES
Input
(X)
Output
(Y)
0
1
2
3
0
-5
-10
-15
YES
INPUT
OUTPUT
Mr. PAL
Function
Rule
Complete the
table using the
following
function rule:
2x + 5 = y
Input
0
1
2
3
Output
2(0) + 5 = 5
2(1) + 5 = 7
2(2) + 5 = 9
2(3) + 5 = 11
Complete the table using the following function rule:
1.
Input
0
1
2
3
y = 2x + 3
Output
2(0) + 3 = 3
2(1) + 3 = 5
2(2) + 3 = 7
2(3) + 3 = 9
2.
y = -4x + 5
Input
0
1
2
3
Output
-4(0) + 5 = 5
-4(1) + 5 = 1
-4(2) + 5 = -3
-4(3) + 5 = -7
3.
Input
0
1
2
3
y = 5x - 1
Output
5(0) - 1 = -1
5(1) - 1 = 4
5(2) - 1 = 9
5(3) - 1 = 14
4.
Input
0
-1
-2
-3
y = 4x - 3
Output
4(0) - 3 = -3
4(-1) - 3 = -7
4(-2) - 3 = -11
4(-3) - 3 = -15
Objective - To graph linear equations.
Graph y = 3x - 4.
x
y
y = 3x - 4
-3
3(-3) - 4
= -13
-2
3(-2) - 4
= -10
-1
3(-1) - 4
= -7
0
3(0) - 4
= -4
1
3(1) - 4
= -1
2
3(2) - 4
=2
3
3(3) - 4
=5
x
This line represents
all the solutions to
y = 3x - 4