Linear and nonlinear functions

Linear and nonlinear functions
Description
Exercise Name:	Linear and nonlinear functions
Math Missions:	8th grade (U.S.) Math Mission
Types of Problems:	3

The Linear and nonlinear functions exercise appears under the 8th grade (U.S.) Math Mission. This exercise helps to draw out the differences between linear functions and non-linear functions.

Types of Problems

There are three types of problems in this exercise:

1. Is the graph linear: This problem proves a function in a graph form. It asks the user to determine whether the graph is linear or not.

   

   Is the graph linear

2. Is the chart linear: This problem proves a function in a chart form. It asks the user to determine whether the graph is linear or not.

   

   Is the chart linear

3. Is the rule linear: This problem proves a function in a rule form. It asks the user to determine whether the graph is linear or not.

   

   Is the rule linear

Strategies

Knowing the three major ways to represent functions (numerical, algebraic and geometric) would increase the ability to perform this exercise well. It is also important to know the difference between lines and non-lines.

1. A graph is a line if it looks like a line, otherwise it is not.
2. A chart represents a line if it shows a constant slope of rise over run.
3. A rule is linear if it can be written in the form ${f(x)=mx+b}$.

Real-life applications

1. Data collected in real-life is often represented in chart form. Being able to recognize when something is linear allows one to know if they can use techniques such as regression from statistics or if they need to pull out something heavier.