Math Problem Statement
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:
Testing the values:
- For input 5: (correct).
- For input 6: (correct).
- For input 8: (correct).
Therefore, if the input is , the output will be:
If you input , the output will be .
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:
- How do we define a function in mathematics?
- Can all functions be expressed as simple arithmetic operations?
- What are other examples of linear functions?
- How do we find the rule of a function from a table of values?
- 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