Understanding Piecewise Linear Functions Worksheet Answers

Piecewise linear functions can be confusing to students, but they don’t need to be. With the help of a worksheet, students can easily understand the concept and be able to answer questions related to it. This article will explain what piecewise linear functions are, how to answer worksheet questions related to them, and provide some example worksheet answers.

What is a Piecewise Linear Function?

A piecewise linear function is a mathematical function that is composed of several linear sections, each of which has a different equation. The equation for each section can be written in the form y=ax+b, where a and b are constants. Each section is defined by two points, and the equation of the line between those points is used to determine the equation of the section.

Answering Piecewise Linear Functions Worksheet Questions

When answering piecewise linear functions worksheet questions, it is important to understand the equation of the line for the section that is being asked about. Once the equation has been determined, the answer can be found by plugging in the given x-value and solving for y. It is also important to pay attention to the given points that define the section, as they can be used to determine the equation of the line.

Example Worksheet Questions and Answers

To help illustrate how to answer piecewise linear functions worksheet questions, here are two example questions and their answers:

Question 1

Given the points (2, 5) and (6, 2), what is the equation of the line for the section defined by these points?

Answer

The equation for the line defined by these points is y=-1x+7. This equation can be determined by plugging the given points into the equation y=ax+b, where a and b are constants, and solving for a and b.

Question 2

Given the equation y=-1x+7, what is the value of y when x=4?

Answer

When x=4, the value of y is 3. This can be determined by plugging 4 into the equation y=-1x+7 and solving for y.

By using worksheets and understanding the concept of piecewise linear functions, students can easily answer worksheet questions related to them. This article has provided two example worksheet questions and their answers to help illustrate how to answer these types of questions.