To start, represent the given points as ordered pairs.
Pattern: Output = Input - 0.5 Table:
Input
Process Column
Output
1
1-0.5
0.5
2
2-0.5
1.5
3
3-0.5
2.5
4
4-0.5
3.5
5
5-0.5
4.5
6
6-0.5
5.5
...
...
...
n
(n)-0.5
n-0.5
Let's start by identifying points on the graph as ordered pairs. An ordered pair can be written in the form ( x, y), where x is the input value and y is the output value.
Now that we have the ordered pairs, let's find a pattern of change by using a table. We need to think about how we can obtain the output values from the input values, so let's use a process column to help us understand what happens between inputs and outputs.
Input
Process Column
Output
1
1- 0.5
0.5
2
2- 0.5
1.5
3
3- 0.5
2.5
4
4- 0.5
3.5
5
5- 0.5
4.5
6
6- 0.5
5.5
...
...
...
n
( n)- 0.5
n-0.5
In the process column, we subtracted - 0.5 from the input values to get the output values. Thus, we can identify the pattern that represents the given graph based on this reasoning.
Pattern
Output = Input - 0.5
