To start, represent the given points as ordered pairs.
Pattern: Output = Input^2 Table:
Input
Process Column
Output
1
1^2
1
2
2^2
4
3
3^2
9
4
4^2
16
5
5^2
25
...
...
...
n
(n)^2
n^2
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
1^2
1
2
2^2
4
3
3^2
9
4
4^2
16
5
5^2
25
...
...
...
n
( n)^2
n^2
In the process column, we raised the input values to the second power to get the output values. Thus, we can identify the pattern that represents the given graph based on this reasoning.
Pattern
Output = Input^2
