How do you determine whether something is a function or not?

If it is a rule or formula that lets you input one number to get another, then it is a function.

To determine whether something is a function or not, you need to check if it fulfills the criteria of a mathematical function. Here's a step-by-step process to determine if something is a function:

1. Understand the concept: A function is a relationship between two sets of numbers, called the domain and the range. It assigns each element from the domain a unique element from the range.

2. Identify the variables: Look for the variables in the given rule, formula, or expression. Functions usually involve at least two variables, such as x and y, or f(x) and x.

3. Input and output: Consider how the variables are related. If you can input a value for one variable and obtain a unique output value for another variable, it suggests that you have a function. In other words, each value in the domain should correspond to exactly one value in the range.

4. Test for uniqueness: To verify if the function is valid, check if each input value produces a single output value. If any input generates multiple outputs, it is not a function.

5. Analyze all scenarios: Sometimes, a function might be defined piecewise, meaning it has different rules or formulas for different ranges of values. In such cases, examine each part separately to see if it satisfies the criteria of a function.

By following these steps, you can determine whether something is a function or not. Remember, the key aspect is that each input value produces a unique output value, making it a one-to-one relationship.