What is a Function?

Guided Notes for this lecture

Learning the terminology of functions will be important for us to be able to communicate about mathematics. In this section we will review the four types of functions we will be studying throughout this course. Pay special attention to any terminology you are not familiar with.

As we study functions it is critically important to understand the relationship between dependent and independent variables. In this next video we will work on understanding that relationship and learning how to identify which is the dependent and which is the independent variable for a formula, table, graph, or word problem.

Sometimes the information we have about the relationship between variables includes information at every point. Sometimes we only have information at some points. We have describe these situations with the terminology "continuous" and "discrete". In the next video we will learn how and when to apply these terms to different functions.

Functions often have restrictions on the numbers that can plugged into them. Functions also have properties that impact what values can be output. This next video defines domain and range for functions.

Functions are sometimes defined over certain sets of numbers. When we notate this mathematically we use interval notation which is outlined in the next video.

When we interpret mathematical information, one goal is to set up a mathematical representation of a scenario. We call this a mathematical model. It is important to learn to set up these models in order to then analyze the model.

Graphical Analysis is an important way in which we understand functions that are graphed. One of key pieces of information we need to understand is the meaning of the intercepts of the graphs. We can also think about what these intercepts mean in other types of functions, which is outlined in the next video.

Another way that we describe functions is based on how they change as we change the independent variable. Below we will learn about the mathematical definition and notation for increasing and decreasing functions.

At the end of this section you should be able to answer the following questions:

1. What are the ways we can describe how a function is behaving?
2. How do we determine and describe any restrictions on a function?
3. What are the four ways we can represent a function?

Check Your Understanding
You should try these problems before reviewing the solutions to these non-graded practice problems.