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Parent Functions and their Graphs

Videos, worksheets, games and activities to help PreCalculus students learn how about parent functions and their graphs.

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More Graphs and PreCalculus Lessons

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 = square root(x), 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) = square root(x), f(x) = cube root(x), f(x) = |x|

This video presents 7 parent functions with equations, graphs, domain, range and asymptotes.
y= x, y = x2, y = square root(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 = sqrt(x), y = 1/x, y = |x|, x2 + y2 = 9 (circle), y = bx

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

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