What the Function?! Graphing Square Root Functions.

What the Function?! Graphing Square Root Functions.

Author: Nate Muckley

Learn how to graph square root functions using a table of values.

A powerpoint on the basics of graphing square root functions, and then examples. Be familiar with making a table of values, and properties of square roots.

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The Graph

The graph of a square root function (y =√x) looks like this: 


...this packet will show you why, and how to create your own graphs!

Domain and Range of square root functions.


     The DOMAIN is all of the possible x values

     The RANGE is all possible y values

I just think of this as where the x or y part of the line is.


*To help remember which one is which (whether domain or range goes to x or y), just think about your friend RAY and his range. The y from Ray's raYnge matches up to the y on the graph.

For square root functions, both the domain and range will extend into infinity, because the line will continue on forever (on graphs, we can only show a portion)

In the basic graph, the domain is greater than or equal to 0, and the range is also greater than, or equal to 0  

Watch out, the beginning will change depending on where the particular graph starts!

Radical Expressions

One phrase your teacher might use is Radical Expression.


A radical expression is everything under the square root symbol.


in the equation

y =   (3x + 2)

(3x + 2) is the radical expression




Graphing Basics

A slide show on the basics of graphing square root functions.


Try out this problem:

y =  √ (2x + 16) + 4

Grab a piece of paper and graph the equation!

(P.S. some easy x-values are: -8, -7.5, -6, -3.5, and 0)


Example Answers