Radical functions and transformations

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Radical functions and transformations

It is always so much easier to tell the domain and range of a function from its graph. In this lesson, we will learn how to graph out a radical function by using a table of value and transformations.


Radical functions: a function which contains a variable inside a root. For example: y=xy = \sqrt x , y=3x5y = {^3}\sqrt{{x - 5}}
y=243x8+11y = 2{^4}\sqrt{{3x - 8}} + 11
  • 1.
    Basic Radical Function: y=xy = \sqrt x
  • 2.
    Transformations of Radical Functions
    For each radical function,
    i) Describe the transformation(s) that should be applied to the graph of y=xy = \sqrt x in order to obtain the graph of the given radical function.
    ii) Write the "Coordinate Mapping Formula", then sketch the graph.
    iii) State the domain and range.
    • c)
      y=x - y = \sqrt x
    • d)
      13y=2x\frac{1}{3}y = \sqrt {2x}
    • e)
      y=2x31+5y = - 2\sqrt {\frac{x}{3} - 1} + 5
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Radical functions and transformations

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