Understanding Function Tables and Basic Relationships
A function table helps organize mathematical relationships between inputs and outputs in a clear, structured format. When working with functions, every input value corresponds to exactly one output value, following a specific rule or pattern.
Definition: A function is a mathematical relationship where each input value (independent variable) produces exactly one output value (dependent variable) based on a specific rule.
The function rule describes how to transform input values into output values. For example, if the rule is "add 6 to the input," then for any input x, the output y would be x + 6. This creates a predictable pattern that can be organized in a function table.
Example: Input (x) | Output (y) = x + 6 0 | 6 1 | 7 2 | 8 3 | 9
When working with linear function tables, it's essential to understand that the relationship between inputs and outputs follows a consistent pattern. This pattern can be expressed as an equation, such as y = mx + b, where m represents the rate of change and b represents the starting value or y-intercept.