A family of functions is merely a set of functions with common characteristics. A parent function is the simplest function that has these common characteristics. Each member of a family of functions is just a changed or transformed parent function. In Algebra 2, you will be introduced to numerous parent functions, including linear, quadratic, exponential, logarithmic, absolute value, square root, and reciprocal functions.

Being familiar with the various parent functions that are part of the Algebra 2 curriculum will make your life easier in high school math! Let me give you a couple of examples of when being familiar with something will make your life easier!

Connecting back to middle school math...

Remember how knowing basic fraction/decimal/percent equivalences helped you in middle school math?

Well, becoming familiar with the parent functions in Algebra 2 - given a table or a graph - will help you in high school math!

1 over 4 1 4 = 0.25 = 25%

2 over 5 2 5 = 0.4 = 40%

1 over 10 1 10 = 0.1 = 10%

Connecting to the real world...

Familiarity with traffic signs is helpful in order to maintain safety on the roads and highways. It's important to know the basics of roadway signs!

The colors of the road signs are important. For example, red indicates stop or prohibition; orange is used for construction or maintenance warning; yellow is used for general warnings; blue is used for tourist information or motorist services.

Traffic Sign: StopTraffic Sign: Detour
Traffic Sign: Handicapped Traffic Sign: Wrong WayTraffic Sign: Merge Left
Source: Traffic Signs, Massachusetts Government

The shapes of the signs are also important. Diamond shaped signs are used to signify warnings; pentagon is used for school crossing signs; circular signs warn of railroad crossings.

Traffic Sign: School ZoneTraffic Sign: Construction ZoneTraffic Sign: Railroad Crossing
Source: Traffic Signs, Massachusetts Government

The basic blue road sign stands for tourist information or motorist services, but these signs can transform or change...based on the symbols or words on the signs.

Traffic Sign: HandicappedTraffic sign: Hospital Traffic sign: Hurrican Evacuation Route
Source: Traffic Signs, Massachusetts Government

Similarly, the basic parent functions you will study in high school mathematics can also change. These changes are called transformations, and you will study those throughout your high school math courses!

 image of graphs with parabolas

Just as traffic signs have distinguishing characteristics, such as shape and color, that aid the driver, so do parent functions in Algebra 2 have distinguishing characteristics that aid the Algebra 2 student! Good drivers recognize these important signs and good Algebra 2 students recognize the parent functions and their corresponding graphs, tables, and symbolic equations.

Just like knowing the shapes and colors of traffic signs helps us on the highway, knowing the basic shapes and facts about parent functions will help you in the Algebra 2 course.

Let's get started learning about the Parent Functions that are part of the Algebra 2 course.