Determine whether each function is a one-to-one function....

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Key Concepts

One-to-One Function

A one-to-one function, also known as an injective function, is one where every element of the function's range is paired with exactly one element of its domain. This means that if the function produces the same output for two different inputs, then those inputs must be identical.

Horizontal Line Test

The Horizontal Line Test is a graphical method used to determine if a function is one-to-one. If any horizontal line intersects the graph of the function at more than one point, the function is not one-to-one.

Domain Restriction

Domain restriction involves limiting the inputs of a function to a certain set. This can be used to ensure that a function becomes one-to-one if it was not injective over its entire natural domain.

Quadratic Function

A quadratic function is a polynomial function of degree two whose graph is a parabola. Quadratic functions are generally not one-to-one when considered over all real numbers due to their symmetry, but they can become one-to-one when their domain is appropriately restricted.

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