# Parent Functions and Parent Graphs Explained — Mashup Math

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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.