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Square root function is a function which is expressed under the radical sign ‘√’. Square root of a function or an expression means that it is raised to an exponent of ‘1/2’. Square root functions can be graphed on an X-Y coordinate plane and we can also find the domain and range of the given function. To graph a square root function, we can plug-in numbers in the place of the variable ‘x’ and find the function or the ‘y’ value for those numbers and plot the points on the plane.
Example 1: Graph the square root function, y = √x.
The function, f(x) = √x is also called as the parent function since other square root functions are derived from it.
Let x = 0, then y = √0= 0. Coordinate point is (0, 0)
Let x= 1, then y= √1 = 1. Coordinate point is (1, 1)
Let x= 2, then y= √2= 1.41. Coordinate point is (2, 1.41)
Let x = 3, then y= √3= 1.73. Coordinate point is (3, 1.73)
The graph looks as shown when the above points are plotted
Example 2: Graph the square root function, y = √(x – 1).
Since the function is (x – 1), hence the graph of y = √x shifts 1 unit to the right.
Let x= 1 then y= √(1- 1)= 0.Coordinate point is (1, 0)
Let x= 2, then y= √(2- 1) = 1. Coordinate point is (2, 1)
Let x= 3, then y= √(3- 1)= 1.41. Coordinate point is (3, 1.41)
Let x= 4, then y= √(4- 1)= 1.73. Coordinate point is (4, 1.73)
The graph looks as shown when the above points are plotted.
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