Math Problem Statement

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

Solution

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:

Output=Input4\text{Output} = \text{Input} - 4

Testing the values:

  • For input 5: 54=15 - 4 = 1 (correct).
  • For input 6: 64=26 - 4 = 2 (correct).
  • For input 8: 84=48 - 4 = 4 (correct).

Therefore, if the input is nn, the output will be:

n4n - 4

If you input nn, the output will be n4n - 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.

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Math Problem Analysis

Mathematical Concepts

Functions
Arithmetic Patterns
Input-Output Relationships

Formulas

Output = Input - 4

Theorems

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Suitable Grade Level

Grades 6-8