Introduction to Functions

A function is a relation between a set of inputs and a set of possible outputs. Each input is related to exactly one output.

Key Concepts

• Domain: The set of all possible inputs for a function.
• Range: The set of all possible outputs for a function.
• Vertical Line Test: A test used to determine if a relation is a function. If a vertical line passes through the graph of the relation at only one point for every x-value in the domain, then the relation is a function.

Notation

A function is often denoted by a letter such as f. The input variable is typically denoted by x, and the output variable is denoted by f(x).

Function Notation

Function notation is a way to represent a function as an equation. For example, if f represents a function, then f(x) = 2x + 3 is the equation for the function.

Examples

Here are some examples of functions:

1. f(x) = 2x + 3
2. g(x) = x² - 1
3. h(x) = √x

Practice Problems

1. Determine the domain and range of the function f(x) = 3x - 1.

2. Use the vertical line test to determine if the relation given by the graph y = x² is a function.

Conclusion

Understanding the concept of functions and their notation is essential for further studies in mathematics. Be sure to practice identifying functions and determining their domains and ranges.