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

**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.

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 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.

Here are some examples of functions:

- f(x) = 2x + 3
- g(x) = x
^{2}- 1 - h(x) = √x

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 = x^{2} is a function.

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.

.Study GuideIntroduction to Functions Activity LessonFunctions Box Worksheet/Answer key

Introduction to Functions Worksheet/Answer key

Introduction to Functions Worksheet/Answer key

Introduction to Functions Worksheet/Answer keyIntroduction to Functions Worksheet/Answer keySlope Worksheet/Answer keyFunction or not? Worksheet/Answer keyIn-and-Out Box

Algebra (NCTM)

Understand patterns, relations, and functions.

Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules.

Represent and analyze mathematical situations and structures using algebraic symbols.

Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope.