Radical functions and transformations

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.

Lessons

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
    a)
    Use a table of values, sketch the graph of the function y=xy = \sqrt x .

    b)
    State the domain and range.


  • 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.
    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