Parent Functions and Representations
Description/Explanation/Highlights
Video Description
This video explains what parent functions and function families are and how they are represented.
Steps and Key Points to Remember
To recognize and represent parent functions, follow these steps:
- A parent function is the most basic form of a function family.
- A function family is a group of functions that share common characteristics.
- For example, \(y=x^2\) is the parent function for the family that we call quadratic. It is the simplest form of the function that has 2 as the largest exponent in the function.
- \(y=x^2+3\) is also in the quadratic family but it is not the parent because it is not the most basic form.
- \(y=x\) is simpler but is not quadratic because its largest exponent is 1 so it does not belong to the quadratic family. It is in fact, the parent for a linear function.
- As stated before functions in the same family share common characteristics. For example, all linear functions have 1 as their largest exponent and form a line when graphed. However, only the parent has a slope of 1 and crosses at the origin.
- Other examples of characteristics are: All quadratics have a 2 as their largest exponent and make a parabola when graphed. Rational functions have a variable in the denominator and asymptotes when graphed. Square root functions have a square root symbol in the equation.
- Functions in the same family have the same shape when graphed as the parent but may be moved around, reflected, stretched or compressed when compared to the parent graph.
- Parents and their families may be represented by tables, graphs, symbolically, or verbally. For more information see the video: Functions and Function Notation.
Here are some key points to keep in mind when recognizing and representing parent functions and their families.
- Parent functions are the most basic form of a function.
- \(y=x^2+3\) is not a parent because it includes +3. It is, however, a part of the quadratic function family that has as its parent \(y=x^2\).
- Function families share common characteristics when graphed or written symbolically.
- Parent functions share a common shape when graphed with other functions in the same family but the other functions may be moved around, reflected, stretched or compressed when compared to the parent.
Video Highlights
- 00:00 Introduction
- 00:26 Definition of a parent function
- 00:40 \(y=x^2\) example of a quadratic parent
- 01:12 Definition of a function family
- 02:47 How parent functions are represented
- 05:33 Conclusion
- To watch this video on YouTube in a new window with clickable highlights, click here