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Common Core (Functions)

Common Core for Mathematics

Examples, solutions, videos, and lessons to help High School students understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range.

If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x.

The graph of f is the graph of the equation y = f(x).

Common Core: HSF-IF.A.1

**Introduction to Functions - Part 1**

Definition of a function, domain, and range.

A function is a rule that for every input assigns a specific output.

The input, usually x, is called the independent variable.

The output, usually y, is called the dependent variable.

The set of all possible inputs is called the domain. The domain is the set of all possible x-values.

The set of all possible inputs is called the range. The range is the set of all possible y-values.

**Introduction to Functions - Part 2**

How to graph a function and how to determine the domain and range of a function.

- f(x) = 4x - 2
- f(x) = x
^{2} - f(x) = |x| - 3

**Determining Domain and Range**

The domain of the function is the set of all x-values, or inputs, of the points on the graph.

The range of the function is the set of all y-values, or outputs, of the points on the graph.

**Determine the Domain and Range Given the Graph of a Function**

Example of how to determine the domain and range of a function given the graph of a function. The domain and range are given using interval notation and using a compound inequality.

**Ex 1: Determine the Domain and Range of the Graph of a Function**

Two examples of how to determine the domain and range of a function given as a graph.

**Ex 2: Determine the Domain and Range of the Graph of a Function**

This video provides two examples of how to determine the domain and range of a function given as a graph.

**Determine if a Relation is a Function**

A function is a correspondence between a first set, called the domain, and a second set, called the range, such that each member of the domain corresponds to exactly one member of the range.

The graph of a function f is a drawing that represents all the input-output pairs, (x, f(x)). In cases where the function is given by an equation, the graph of a function is the graph of the equation y = f(x).

**Ex 1: Determine if the Graph of a Relation is a One-to-One Function**

How to use the vertical line test and the horizontal line test to determine if the graph of a relations is a one to one function.

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