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
is a function from a family of functions that is in its simplest form
—meaning that it has not been transformed at all.
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
) and that the function y=x+3 is a transformed version
of the parent function (it was shifted 3 units upward).