What you’ll learn to do: Write and interpret a linear function

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 species of bamboo. 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.^[1] 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 that a function is a relation that assigns to every element in the domain exactly one element in the range. A linear function is 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.