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Functions MAT/117 Version 9

University of Phoenix Material

Functions The focus of this week is to learn more about functions and to work with nonlinear equations. A function is

a relationship between two variables; one variable is called the input (or x) and the other variable is the

output (or y). The basic idea of a function is that every input has exactly one output. Learn more about functions with the video “Introduction to Functions” from Khan Academy (go to CME > Building Math Confidence > Math Videos > Khan Academy).

Types of Functions

Functions are used to model data, so patterns or trends can be identified from the data. For that reason, it’s necessary to identify the different types of functions to be able to describe the data. Here is a list of the most typical functions and its graphs:

Name of the Function Function Form Graph

Linear

Quadratic

Cubic

Rational

http://www.khanacademy.org/math/algebra/algebra-functions/v/introduction-to-functions

Functions MAT/117 Version 9

Radical √

How to Find the Domain and the Range

The graph of a function is a continuous line or curve. The domain of a continuous line or curve will be

from the smallest x-coordinate where the graph starts to the largest x-coordinate where the graph ends,

when reading the x-axis from left to right. The range of a continuous line or curve will be from the smallest

y-coordinate where the graph starts to the largest y-coordinate where the graph ends, when reading the

y-axis from bottom to top. See the graph below.

Operations with Functions

We can perform the below basic operations with functions. Let and – . Addition:

Example:

Let and –

–

Functions MAT/117 Version 9

Subtraction:

Example:

Let and –

–

Multiplication:

Example:

Let and –

–

Division:

Example:

Let and –

(This rational expression cannot be simplified more).

The above operations with functions are performed in the same manner as you did with polynomials.

Functions MAT/117 Version 9

Zero Product Property

This property states that if a multiplication results in zero, then it means one of the factors must be zero.

Algebraically this property is written as AB = 0, then A = 0 or B = 0. This property is essential when solving quadratic equations by the factoring method, which you will learn in Cognitive Tutor.