https://file.aiquickdraw.com/mathbot/file/172902722859512tqu7qi.jpg

Looking at the image you uploaded, you are working on a question that provides a table of inputs and outputs, and you're asked to determine the output when the input is \( n \). Let's break it down.

The input/output table is as follows:

| Input  | Output  |
|--------|---------|
|   5    |    1    |
|   6    |    2    |
|   8    |    4    |
|   \( n \) |   ?   |

You need to find the output for input \( n \).

### Step-by-Step Analysis:

1. **Find a Pattern:** 
   - From the table, notice the relationship between input and output. Let's check if there’s an arithmetic or other functional relationship:
     - For \( 5 \rightarrow 1 \), the difference is \( -4 \).
     - For \( 6 \rightarrow 2 \), the difference is \( -4 \).
     - For \( 8 \rightarrow 4 \), the difference is also \( -4 \).

   So, it seems the output is related to the input by subtracting \( 4 \).

2. **Assume General Function:** 
   The pattern suggests that the output could be \( \text{output} = \text{input} - 4 \).

3. **Apply to \( n \):**
   - If the input is \( n \), using the relationship \( \text{output} = n - 4 \), the output for input \( n \) would be:
   \[
   n - 4
   \]

Thus, the correct output when the input is \( n \) should be \( n - 4 \).

Would you like any further details or clarification?

### Related Questions:
1. What if the pattern changed after input 8? How would you adapt your approach?
2. Can you think of another mathematical relationship that could fit these points?
3. How would the answer change if the function involved multiplication instead of subtraction?
4. What if you were given additional points? Could you use interpolation to determine the function?
5. How would this approach differ for a non-linear pattern?

**Tip:** Always check for common differences or ratios between values to identify possible relationships in function tables.

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

Learn how to find the output of a function based on an input-output table. In this problem, the input-output relationship follows a simple linear pattern: output = input - 4. Suitable for students in Grades 6-8.

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