Square root functions can be represented in multiple ways. In this lesson, you will learn how to generate one representation of a square root function when you are given another representation of the same function. The representations can be algebraic, tabular, graphical, or a verbal description. Let's first review what a square root function is.

The parent square root function as an equation is y = √x.

• To represent this in a table, choose 3 or 4 values for x. You can use your graphing calculator to obtain "nice" numbers, or you can go to the following GTable applet by clicking on the image below. For directions on how to use the applet, you can Interactive popup. Assistance may be required. click here. Direction to create a table: Click on "Add Expression" to be able to add the expression you would like to use. You do not need to type in the "y=". In order to enter a square root function, you need to type "sqrt" to represent the radical sign. For example to make a table for y = √x, you would type sqrt(x). To make a table which friendlier numbers, change the low value to -20, the high value to 20, and the subdivision value to 40. Close

  
  

  For this problem, I will choose 0, 1, 4, and 9. When you substitute 0 in for x, you get 0 for y. When you substitute 1 in for x, you get 1 for y. When you substitute 4 in for x, you get 2 for y, and when you substitute 9 in for x, you get 3 for y.

  X	Y
  0	0
  1	1
  4	2
  9	3

  To represent this verbally, we can say that the x value is the square of the y value. In a previous lesson you learned about inverse functions. This is an example of that concept. To review inverse functions, you can go to Algebra II, Module 3, Lesson 8.

  To represent this graphically, we can also use these same x and y values to graph these points on a coordinate grid.

  

  We have just represented the parent square root function in 4 different ways, algebraically, tabular, verbally, and graphically.