Basic radical functions

Basic radical functions

A radical function is a function that contains a variable inside a root. By graphing out a radical function, we can easily find out its domain and range.

Lessons

  • 1.
    Introduction to Radical Functions
    • What is a radical function?
    • A radical functions is 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

  • 2.
    Basic Radical Function: y=xy = \sqrt x
    a)
    Use a table of values, sketch the graph of the function y=xy = \sqrt x .

    b)
    State the domain and range.


  • 3.
    For each radical function,
    i) Describe the transformation(s) that should be applied to the graph of y= 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.
    a)
    y2=x+3y-2 = \sqrt x+3

    b)
    y=xy = \sqrt -x

    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