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Guides d'étude > College Algebra

Introduction to Linear Functions

Learning Objectives

By the end of this lesson, you will be able to:
  • Represent a linear function.
  • Determine whether a linear function is increasing, decreasing, or constant.
  • Write and interpret a linear function.
 
An upward view of bamboo trees. A bamboo forest in China (credit: "JFXie"/Flickr)
Imagine placing a plant in the ground one day and finding that it has doubled its height just a few days later. Although it may seem incredible, this can happen with certain types of bamboo species. These members of the grass family are the fastest-growing plants in the world. One species of bamboo has been observed to grow nearly 1.5 inches every hour.[footnote]http://www.guinnessworldrecords.com/records-3000/fastest-growing-plant/[/footnote] In a twenty-four hour period, this bamboo plant grows about 36 inches, or an incredible 3 feet! A constant rate of change, such as the growth cycle of this bamboo plant, is a linear function. Recall from Functions and Function Notation that a function is a relation that assigns to every element in the domain exactly one element in the range. Linear functions are a specific type of function that can be used to model many real-world applications, such as plant growth over time. In this chapter, we will explore linear functions, their graphs, and how to relate them to data.

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