In Exercises 21-42, determine whether each function is a...

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Key Concepts

One-to-One Function (Injective Function)

A one-to-one function, also known as an injective function, is a function where each element of the domain maps to a unique element in the range. In other words, no two distinct inputs share the same output, ensuring that every output is associated with exactly one input, which is critical for the function to have an inverse on its image.

Horizontal Line Test

The horizontal line test is a graphical method for determining whether a function is one-to-one. If every horizontal line intersects the graph of the function at most once, the function is injective. This test provides an intuitive way to verify the uniqueness of outputs for different inputs.

Function

A function is a fundamental concept in mathematics that describes a relation where each element in the domain is paired with a single element in the range. Understanding functions and their properties, such as injectivity, is essential for topics in algebra, calculus, and beyond.

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