Equations, Tables and Graphs

1
Equations, Tables and Graphs

• Graphing Activity

2
Warm UP
Determine if the following relations are
functions and be able to explain why or why not
3.
1.
2.
Input
Output
x y
-2 5
-1 2
0 4
1 3
2 5
1 2 3 4
2 3 4
4. ( 1, 2) ( 2, 3) ( 3, 2) ( 4, 4)
3
Create a table and a graph from the following
equations then determine if it is a function,
then determine if it is linear or non-linear
1.
7.
8.
2.
9.
3.
10.
4.
11.
5.
12.
6.
4
1
x y





x y
-2 -5
-1 -4
0 -3
1 -2
2 -1
No repeats in x values
(Circle correct response)
Function Yes No
Linear Yes No
5
2
x f(x)





x f(x)
-2 6
-1 5
0 4
1 3
2 2
No repeats in x values
(Circle correct response)
Function Yes No
Linear Yes No
6
3
x y





x y
-2 -4
-1 -7
0 -8
1 -7
2 -4
No repeats in x values
(Circle correct response)
Function Yes No
Linear Yes No
7
4
x y





x y
-6 -5
-3 -4
0 -3
3 -2
6 -1
No repeats in x values
(Circle correct response)
Function Yes No
Linear Yes No
8
5
x y
-2
-1
0
1
2
x y
-4 -2
-1 -1
0 0
-1 1
-4 2
There are repeats in x values
(Circle correct response)
Function Yes No
Linear Yes No
9
6
x y





x y
-2 2
-1 3
0 4
1 3
2 2
No repeats in x values
(Circle correct response)
Function Yes No
Linear Yes No
10
7
x f(x)





x f(x)
-2 4
-1 3
0 2
1 1
2 0
No repeats in x values
(Circle correct response)
Function Yes No
Be careful to include enough values to see the
shape. Try 3 for x and see y1. This gives you
the classic absolute value V shape
Linear Yes No
11
8
x y





x y
-2 0
-1 -2
0 -4
1 -6
2 -8
No repeats in x values
(Circle correct response)
Function Yes No
Linear Yes No
12
9
x y





x y
-2 1/4
-1 1/2
0 1
1 2
2 4
No repeats in x values
(Circle correct response)
Function Yes No
Linear Yes No
13
10
x y





x y
-2 -8
-1 -5
0 -4
1 -5
2 -8
No repeats in x values
(Circle correct response)
Function Yes No
Linear Yes No
14
11
x y
5
5
5
5
5
x y
-2 5
-1 5
0 5
1 5
2 5
No repeats in x values
(Circle correct response)
Function Yes No
Linear Yes No
15
12
x y
-3
-3
-3
-3
-3
x y
-3 -2
-3 -1
-3 0
-3 1
-3 2
There are repeats in x values
(Circle correct response)
Function Yes No
Linear Yes No
16
Summary
Function Linear
Function Linear
1.
7.
Yes No
Yes Yes
Yes Yes
8.
2.
Yes Yes
9.
Yes No
Yes No
3.
10.
Yes Yes
Yes No
4.
11.
Yes Yes
No No
5.
12.
No Yes
Yes No
6.
Are there any patterns you see from the equations
to help you determine functions and or linear
relationships?