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Step Functions and Piecewise Functions

In these lessons, we will learn how to graph and solve Step Functions and Piecewise Functions.

We have a Piecewise function calculator that can graph piecewise functions. We will learn how to use the TI 83/84 graphing calculator and how to avoid some Common Algebra Mistakes.

This lesson is part of a series of free, online Intermediate Algebra Lessons or Algebra II lessons.

In addition, we have videos, worksheets, and activities to help Algebra students.

Step Functions

Some functions are not easily written as a formula. On a graph, a step function looks like a flight of stairs. The graphs of step functions have lines with an open circle on one end and a closed circle on the other to indicate inclusion, like number line inequality graphs. A rounding step function tells us to round a decimal number to the next whole integer or the previous whole integer.

This video shows how to solve a step function for a specific value.
This video shows how to graph a step function.

Piecewise Functions

In real world situations it can be difficult to describe events with a single smooth function. We sometimes need to use piecewise functions to describe these situations. Piecewise functions are functions that are defined to be smooth functions for specific intervals of the independent variable, most commonly the x-variable.

Graphing Piecewise Defined Functions - 2 examples are shown.
Graphing a Piece-Wise Defined Function - Another Example.

An Introduction to piecewise functions.
Examples of piecewise functions. These examples are designed to highlight certain important aspects of piecewise functions.

Piecewise Function Calculator

Enter Function 1 and Function 2 with Domains and obtain a graph of piecewise function. Use it to check your answers.

Using a Graphing Calculator

One tool used throughout Algebra, Trigonometry, and Calculus is a graphing calculator. One thing using a graphing calculator is helpful for is solving systems of equations. We can solve systems of linear equations by using a graphing calculator and matrices. We can also solve systems of nonlinear equations by using a graphing calculator to graph their equations and find the intersection.

Introduction to entering expressions on the graphing TI 83/84 graphing calculator.


Common Algebra Mistakes

Some of the most common algebra mistakes come from misunderstanding the order of operations or what is commonly known as PEMDAS. We must keep in mind that the multiplication and division are done at the same time in the order of operations, as are addition and subtraction. The most important way to help not make these common algebra mistakes is by practicing and being aware of pitfalls.

Dr. Pan goes through the most common algebra mistakes and shows corrections.
Dr. Pan goes through common algebra errors.

Dr. Pan goes through other common algebra errors.
Dr. Pan goes through the most common algebra mistakes and shows corrections.

Dr. Pan goes through the most common algebra mistakes and shows corrections.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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