What does something have to be inorder to be considered a function.
I'm not talking about the verticle line test or somethng to verify, im saying in words. like can it not be negative or somehting?
I did it further down.
generally speaking, if for any x you pick a unique value of y is determined by your equation, then the relation is a function
e.g., y = x^2 is a function.
any x you choose yields only one y value
but
x = y^2 is NOT a function because x = 9 yields 2 values of y, namely ±3
To be considered a function, something must meet the following criteria:
1. Each input must have only one output: For every input value, there should correspond exactly one output value. In other words, an input cannot produce multiple different outputs in a function.
2. Consistent behavior: A function should produce the same output for the same input value every time it is evaluated. For example, if you input 5 and get an output of 10, you should always get the same output of 10 whenever you input 5 into the function.
3. Defined domain and range: A function must have a defined set of input values (domain) and output values (range). The domain may be restricted, such as only allowing positive numbers or excluding certain numbers like zero. However, the range can contain any value, including negative numbers.
4. No "broken" or undefined behavior: A function should not encounter any undefined cases or "broken" behavior. For example, dividing by zero or taking the square root of a negative number results in undefined behavior and cannot be considered a function.
It is important to note that whether a function can or cannot be negative depends on the context and mathematical operations involved. A function can certainly have negative outputs if the mathematical relationship allows for it.