https://file.aiquickdraw.com/mathbot/file/1729207115998gydjafgg.jpg

The table shows the relationship between the input and output values of a function. Let's break it down step by step to figure out the pattern:

- Input: 5, Output: 1
- Input: 6, Output: 2
- Input: 8, Output: 4

The relationship between the input and output seems to follow a consistent mathematical pattern. The output appears to be increasing by 1 for every increase of 1 in the input from 5 to 6, and by 2 when the input increases from 6 to 8.

One possible pattern is that the output corresponds to the formula:

\[
\text{Output} = \text{Input} - 4
\]

Testing the values:
- For input 5: \(5 - 4 = 1\) (correct).
- For input 6: \(6 - 4 = 2\) (correct).
- For input 8: \(8 - 4 = 4\) (correct).

Therefore, if the input is \(n\), the output will be:

\[
n - 4
\]

If you input \(n\), the output will be \(n - 4\).

Let me know if you need further explanation, or if you'd like details on a specific point.

Here are 5 relative questions you might want to explore:
1. How do we define a function in mathematics?
2. Can all functions be expressed as simple arithmetic operations?
3. What are other examples of linear functions?
4. How do we find the rule of a function from a table of values?
5. What happens if the function's pattern is nonlinear?

**Tip**: When looking for patterns in functions, try comparing changes in input and output values to find arithmetic or geometric relationships.

Below is the table of values of a function. Write the output when the input is n.

Learn how to determine the output of a function when the input is n using a table of input-output values. The solution demonstrates a clear arithmetic pattern where the output is calculated as input minus 4. Suitable for students in Grades 6-8.

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