Introduction to Functions in Algebra

This page provides an overview of functions in Algebra 1, covering key concepts and examples to help students understand and work with functions. The content includes definitions, examples of functions and non-functions, linear function equations, and practice problems.

Definition: A function is a relationship between inputs and outputs where each input is associated with exactly one output.

The page illustrates the concept of functions using coordinate pairs and graphs. It emphasizes that for a relation to be a function, all x-values (inputs) must be different.

Example: The coordinate pairs (2,3), (4,2), (7,3), (4,5) do not represent a function because the x-value 4 is repeated with different y-values.

The document introduces linear function equations and provides examples of how to evaluate them. It shows the general form of a linear function: f(x) = 2x + 5, and demonstrates how to calculate f(-2).

Highlight: When evaluating a function, replace all instances of x in the equation with the given input value.

Non-linear functions are also briefly mentioned, with an example of a quadratic function: G(x) = x² - 2x.

Vocabulary: Non-linear functions are those whose graphs are not straight lines, such as quadratic or exponential functions.

The page includes several practice problems for students to work on, reinforcing the concepts of function evaluation and notation. These problems range from simple linear functions to more complex expressions involving squares and constants.

Example: For the function f(x) = 2x + 5, calculate f(-2): f(-2) = 2(-2) + 5 = -4 + 5 = 1

This comprehensive introduction to functions provides a solid foundation for students beginning their study of Algebra 1 functions. The mix of definitions, examples, and practice problems helps reinforce understanding and prepares students for more advanced topics in algebra and function analysis.