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# ZingPath: Concepts of Function

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## Concepts of Function

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### Lesson Focus

#### Determining Whether a Relation is also a Function

Algebra-1

You will use various representations of relations to show what makes a relation a function.

### Now You Know

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

• Determine whether a relation is a function or not when the relation is described by a verbal rule, an equation, a table or a Venn diagram.
• Determine whether a relation is a function or not when the relation is represented on a graph

### Everything You'll Have Covered

Function terminology explained

A function is a dependency between the elements of two sets. The first set, the independent variable, is called the domain and is also referred to as the input variable. The second set, the dependent variable, is called the range and is also referred to as the output variable.

Here is an example. You go to a cell phone provider and are told the plan you want is \$25.00 a month plus \$0.15 cents for each text message. You tend to send eight or less text messages a month. The number of text messages is the independent variable; the dependent variable is the total cost per month. This function is represented below using a graph, equation, table, and mapping diagram.

Relation = (number of test messages, total cost)

y = 25.00 + 0.15x

Relation as a Function

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

The above example represents a function because all the criteria are met.

Expressing functions

Functions can be expressed using a verbal rule, an equation, a graph, and with a table or a mapping diagram. An example follows:

Verbal rule: B = {(x, y): 3x = y, where x and y are positive integers and x is less than or equal to 4}

Equation: f(x) = 3x with Domain = {1, 2, 3, 4}

Table:

Graph:

Mapping diagram:

### Tutorial Details

 Approximate Time 20 Minutes Pre-requisite Concepts Learners should be familiar with the basic properties of sets, basic understanding of relations, graphing relations Course Algebra-1 Type of Tutorial Skills Application Key Vocabulary functions, graphs of functions, relation