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: $y = \sqrt x$ , $y = {^3}\sqrt{{x - 5}}$
$y = 2{^4}\sqrt{{3x - 8}} + 11$
• 1.
Basic Radical Function: $y = \sqrt x$
a)
Use a table of values, sketch the graph of the function $y = \sqrt x$ .

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 $y = \sqrt x$ 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)
$y - 2 = \sqrt {x + 3}$

b)
$y = \sqrt { - x}$

c)
$- y = \sqrt x$

d)
$\frac{1}{3}y = \sqrt {2x}$

e)
$y = - 2\sqrt {\frac{x}{3} - 1} + 5$