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# ZingPath: Concepts of Function

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## Concepts of Function

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### Lesson Focus

#### The Concept of Function

Algebra Foundations

You will identify a function, the domain (input, independent variable) and range (output, dependent variable), and the properties to determine a function.

### Now You Know

After completing this tutorial, you will be able to complete the following:

• Define a function.
• Identify dependent and independent variables.
• Identify the domain (input) and range (output) of a function.
• Apply the properties for determining a function.

### Everything You'll Have Covered

A function is a dependency between the elements in two sets. The first set, with the independent variables, is called the domain and is often referred to as the input. The second set, with the dependent variables, is called the range and is often referred to as the output.

We will take a look at a simple example. We are considering riding 3 rides at a carnival. Each ride has a height restriction. The height restrictions are 48 inches and 36 inches, depending on the ride. The independent variables are the rides and the dependent variables are the height restrictions required by the type of ride. The domain (input) and range (output) are shown in the following graphic.

Function defined

A function is a relation where every input has an output and each input has only one output. No element in the domain is left unmapped. No element in the domain is mapped to more than one element in the range.

Look back at the carnival ride example. The example represents a function. All criteria are met.

Expressing functions

Functions are often expressed by a rule with a domain then charted. They are also expressed in mapping diagrams. An example follows.

The following key vocabulary terms will be used throughout this Activity Object:

·       dependent variable - the result of the independent variable being changed; often, x is used for the independent variable and y for the dependent variable because y depends on the value of x

·       domain - the set of input values for which a function is defined

·       function - a special type of relationship in which each element of the domain is paired with exactly one element of the domain

·       independent variable - a variable whose values are independent of changes in the values of other variables, denoted by x in a function given by y = f(x)

·       input - the elements that define the domain set

·       output - the elements that define the range set

·       range - set of all output values produced by a function

·       relation - any set of ordered pairs of inputs and outputs

·       set - a collection of objects or elements

### Tutorial Details

 Approximate Time 10 Minutes Pre-requisite Concepts Students should know the definitions of domain, equation, function, functional notation, fraction, input, output, relation, range, set, square, and table of values. Course Algebra Foundations Type of Tutorial Concept Development Key Vocabulary dependent variable, domain, function