Functions

A function is an algebraic equation that relates one variable (the input or independent variable) to another variable (the output or dependent variable). Recall that the equation of a line has a format y = mx + b.  This line equation can also be expressed in function notation as f(x) = mx + b. 

For example, let’s say we have the equation of a line given by the formula y = 3x – 5.  In functional notation, this line equation will be represented as f(x) = 3x – 5.  When we evaluate this function when x = 2, we get f(2) = 3(2) – 5 = 6 – 5 = 1.

In this section of the Math Hub, you will find several videos dealing with different types of functions.  The complete transcript along with copious examples is provided here: 

In these videos, you will learn the following:

• How to differentiate between differ types of functions.
• How to evaluate functions.
• How to determine the intercepts and asymptotes of functions. 

This first video provides an overview of functions.

The following videos provide demonstrations of different kinds of functions. 

Power functions are demonstrated in the following video.  Power functions contain components where variables in the equation are raised to a power.  For example, quadratic functions have a leading element where the variable is raised to the power of 2 while cubic functions will have a leading element where the variable is raised to the power of 3.  In this lecture, you will learn how to determine the domain and range of a power function.

Radical functions are explored in the video below.  A radical function is something that has the form f(x)=nx.  In this presentation, you will learn how to determine the domain and range of a radical function. This video also includes an introduction to the nature of imaginary numbers where i=-1.

This video demonstrates how to work with rational functions.  Basically, a rational function is in the form of a fraction so they will look something like the following f(x)=A(x)B(x).  In addition to finding the domain and range of these functions, you will also learn that rational functions have asymptotes.  Asymptotes are lines where the function would result in the undefined format 10.  

The final presentation this week introduces absolute value functions.  These are functions that contain the absolute value symbol which means they are in the following form: f(x)=x. In this video, you will learn how to determine the domain and range of an absolute value function.