- #1
FizX
- 9
- 0
What does it mean for a function to be unique?
A unique function is a mathematical function that has only one output for each input. This means that for every value of x, there is only one value of y that satisfies the function.
A function is unique if it passes the vertical line test. This means that a vertical line drawn through the graph of the function will only intersect the graph at one point, indicating that there is only one output for each input.
No, a function cannot be both unique and non-unique. It is either unique or it is not. A function may have multiple outputs for a single input, in which case it is considered non-unique.
A unique function and a one-to-one function are the same thing. They both have only one output for each input. However, the term one-to-one is often used to emphasize the fact that each input has a unique output, while unique function simply refers to the function having only one output for each input.
Yes, a function can still be unique even if it has a horizontal asymptote. The horizontal asymptote only applies to the behavior of the function as x approaches positive or negative infinity, but does not affect the uniqueness of the function for other input values.