one-to-one function
[one-to-one function|one-to-one function] A one-to-one function is a function where each output value corresponds to exactly one input value.
Definition
one-to-one function A one-to-one function is a function where each output value corresponds to exactly one input value. In such a function, every input maps to a unique output, and the inverse of the function is also a function. The inverse function satisfies the property that applying it to the output of the original function returns the original input.
Mechanism
one-to-one function The function in part (b) shows a relationship where each input is associated with a single output, establishing a one-to-one function. This type of function allows for the evaluation of its inverse at specific inputs. A complete representation of the inverse function can be constructed in many cases when dealing with one-to-one functions.
Causes
one-to-one function The <a href='/en/entity/horizontal-line'>horizontal line test</a> provides an easy method to determine if a graph defines a one-to-one function. Once the graph is confirmed to define a function, applying this test helps identify whether it meets the criteria for a one-to-one relationship. The test involves checking if any horizontal line intersects the graph at more than one point.
Effects
one-to-one function The <a href='/en/entity/horizontal-line'>horizontal line test</a> provides an easy method to determine if a graph defines a one-to-one function. Once the graph is confirmed to define a function, applying this test helps identify whether it meets the one-to-one criteria. A one-to-one function ensures each input corresponds to a unique output, as demonstrated by the example where each input is associated with a single output.