School

Victor Valley College **We aren't endorsed by this school

Course

MATH 120

Subject

Mathematics

Date

Nov 13, 2023

Type

Other

Pages

14

Uploaded by LieutenantElectronWaterBuffalo5 on coursehero.com

December 8, 2022
Parent Functions and Parent Graphs Explained!
mashupmath.com
/blog/parent-function-graphs-explained
What are Parent Functions and Parent Function Graphs?
Learning about
parent functions
and
parent graphs
will give you better insight into the
behaviors of a myriad of other functions that you will often come across in algebra and
beyond. Your conceptual understanding of parent functions and their graphs is the key to
working out transformations of equations and graphs.
The following free guide to
Parent Functions and Their Graphs
will explain what parent
functions are, what their graphs look like, and why understanding their behavior is so
important in math. In this post, we will explore the parent functions of the following
commonly occurring functions:
Absolute Value Parent Function
Linear Parent Function
Quadratic Parent Function
Cubic Parent Function

Exponential Parent Function
Inverse Parent Function
Square Root Parent Function
By the end of this guide, you will be able to identify the parent function of a function, use it
to sketch graphs, and determine the function associated with a graph with ease!
Before you learn about parent functions and parent function graphs, let's do a quick recap
of some key vocabulary terms and definitions related to parent functions.
What is a parent function? What is a parent graph?
In math, a
parent function
is a function from a family of functions that is in its simplest form
—meaning that it has not been transformed at all.
A
parent graph
is the graph of a parent function on the coordinate plane.
While these definitions may sound confusing at first glance, the concepts are actually pretty
simple when you look at them visually.
For example, let's consider the liner functions y=x and y=x+3.
In this case, the family of functions is the linear function (any function of the form y=mx+b)
that represents a line of the coordinate plane.
So, in this case, y=x is the linear parent function, and y=x+3 is just a transformed version of
the parent function (because it was shifted up three units from the original parent function's
position on the graph).
Again, notice that the function y=x is the
linear parent function
(the line y=x on the
coordinate-plane is the
parent graph
) and that the function y=x+3 is a transformed version
of the parent function (it was shifted 3 units upward).

All Parent Functions...
If you understand the linear parent function and what it represents, then you can
understand all parent functions.
The animated GIF to the right further demonstrates what a linear parent function is and
how it relates to all other linear functions.
The key takeaway right now is that every function family (linear, quadratic, cubic, square
root, etc.) has a parent function which all other functions in that family can be derived from
simply by transforming the basic parent function.