What type of function allows the output to be uniquely determined by the input?

A function that allows the output to be uniquely determined by the input is known as a one-to-one function. In a one-to-one function, each input corresponds to exactly one output, and each output is produced by exactly one input. This means that no two different inputs can yield the same output, which is a key characteristic of one-to-one functions.

For example, the function (f(x) = 2x + 3) is one-to-one because for every value of (x), there is a distinct output (f(x)). If you imagine inputting 1, you get 5; if you input 2, you get 7. No two different values of (x) will produce the same (f(x)) value.

Other types of functions may not exhibit this unique mapping. For instance, many polynomial functions can produce the same output for different inputs (consider (x^2)), and while linear and quadratic functions are specific examples of polynomial functions, they can also have outputs that repeat for different inputs. Hence, they do not necessarily guarantee that every input maps to a unique output in the same way a one-to-one function does.

Understanding the properties of functions helps clarify their behaviors and how