Looking at the table provided, we need to find a pattern that explains how the input is transformed into the output. The inputs are $5, 8, 9$ and the corresponding outputs are $7, 10, 11$.

By observing the pattern:

• When the input is $5$, the output is $7$.
• When the input is $8$, the output is $10$.
• When the input is $9$, the output is $11$.

The relationship between input and output can be expressed as: $\text{Output} = \text{Input} + 2$ For every input, the output is the input value increased by 2.

Therefore, when the input is $n$, the output will be: $\text{Output} = n + 2$

Would you like more details or explanations?

Here are 5 related questions to expand your understanding:

1. How would the output change if the relationship was subtraction instead of addition?
2. Can you create a different rule where the output is less than the input?
3. What happens if we multiply the input by a constant instead of adding?
4. How would you find the output if $n$ was a large number, say 1000?
5. What if the pattern wasn't consistent—how would you identify the rule then?

Tip: When analyzing a function from a table of values, always check for simple arithmetic operations like addition, subtraction, multiplication, or division to find the pattern.