Parent Functions And Their Graphs


Lessons with videos, examples and solutions to help PreCalculus students learn how about parent functions and their graphs.




Share this page to Google Classroom

Related Pages
More Graphs And PreCalculus Lessons
Graphs Of Functions

The following figures show the graphs of parent functions: linear, quadratic, cubic, absolute, reciprocal, exponential, logarithmic, square root, sine, cosine, tangent. Scroll down the page for more examples and solutions.

Graphs of parent functions

The following table shows the transformation rules for functions. Scroll down the page for examples and solutions on how to use the transformation rules.

Transformation rules for graph functions




Parent Functions And Their Graphs - How To Graph Elementary Functions?

In math, we often encounter certain elementary functions. These elementary functions include rational functions, exponential functions, basic polynomials, absolute values and the square root function. It is important to recognize the graphs of elementary functions, and to be able to graph them ourselves. This will be especially useful when doing transformations.

Basic Graphs That Every Algebra Student Should Know

Basic graphs that are useful to know for any math student taking algebra or higher.
y = mx + b (linear function)
y = x2 (quadratic)
y = x3 (cubic)
y = x5
y = |x| (absolute)
y = √x (square root)
y = 1/x (reciprocal)
y = 1/x2
y = logb(x) for b > 1
y = ax for a > 1 (exponential)
y = ax for 0 < a < 1

The Graphs Of Six Basic Functions That You Should Know

f(x) = x
f(x) = x2
f(x) = x3
f(x) = √x
f(x) = cube root(x)
f(x) = |x|

7 Parent Functions With Equations, Graphs, Domain, Range And Asymptotes

y = x
y = x2
y = √x
y = x3
y = 1/x
y = 1/x2
y = |x|



Exploring Properties Of Parent Functions

In math, every function can be classified as a member of a family. Each member of a family of functions is related to its simpler, or most basic, function sharing the same characteristics. This function is called the parent function.

This lesson discusses some of the basic characteristics of linear, quadratic, square root, absolute value and reciprocal functions.

Transformations Of Parent Functions

Learn how to shift graphs up, down, left, and right by looking at their equations.

Vertical Shifts:
f(x) + c moves up,
f(x) - c moves down.

Horizontal Shifts:
f(x + c) moves left,
f(x - c) moves right.

Transforming Graphs And Equations Of Parent Functions

Looking at some parent functions and using the idea of translating functions to draw graphs and write equations.

y = x,
y = x2,
y = x3,
y = √x,
y = 1/x,
y = |x|,
x2 + y2 = 9 (circle),
y = bx



Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
Mathway Calculator Widget



We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.