Here's a breakdown:
* Function: A function is a rule that assigns exactly one output value to each input value.
* Input: The value you put into the function (often represented by 'x').
* Output: The value you get out of the function (often represented by 'y').
* Rule: The specific mathematical formula or equation that defines the relationship between the input and output.
Examples of function rules:
* y = 2x + 1: This rule tells you to double the input value (x) and then add 1 to get the output value (y).
* f(x) = x^2: This rule tells you to square the input value (x) to get the output value.
* g(x) = |x|: This rule tells you to find the absolute value of the input value (x) to get the output value.
Key points:
* A function rule must be a well-defined mathematical expression.
* The function rule must be consistent for all input values.
* The function rule can be expressed in different forms (e.g., equation, table, graph).
In essence, the function rule is the heart of a function, dictating how the input is transformed into the output.