Radical Functions: Graphing Radical Functions and Domain and Range

Graphing Square Root Functions

You have already learned about the transformations of the quadratic functions when the values of "a", "h", and "k" are changed. These transformations are the same for square root functions, with the addition of a "b" value. Analyze the following diagram to learn more about the transformation of square root functions.

Image of y equals a times the square root of b times the quantity x minus h plus k. a value: Horizontal stretch of compression by a factor of the absolute value of 1 divided by b. For b is less than 0 the graph is reflected across the y-axis. b value: Vertical stretch or compression by a factor of the absolute value of a. For a is less than 0 the graph is reflected across the x-axis. h value: Horizontal translation. If h is less than 0 the translation is the absolute value of h units to the left. If h is greater than 0 the translation is the absolute value of h units to the right. k value: Vertical translation. If k is greater than 0 the translation is the absolute value of k units up. If k is less than 0 the translation is the absolute value of k units down.

 

These same rules apply for cube root functions.