What is the relationship between the input and output values in the function table, and what is the function rule that governs the relationship?

In a function table, the relationship between the input and output values is determined by a function rule. The function rule defines how the input values are transformed into output values.

To understand the relationship and identify the function rule, you need to analyze the given function table. Look for patterns or trends in the input and output values. Consider how the values in the input column correspond to the values in the output column.

Typically, you can start by examining the differences between consecutive input and output values. For example, if the input values increase by a constant amount each time, this could indicate a linear relationship. If the output values double each time the input values increase by 1, it may suggest an exponential relationship.

Additionally, you can try plugging in some known input values into the function rule, and compare the calculated output values with the ones in the table. This process will help you identify the equations or patterns governing the relationship.

Once you have identified the pattern or equation, you can write it as the function rule. The function rule will describe mathematically how the input values are related to the output values in the function table.