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.
• What is a radical function?
• A radical functions is a function which contains a variable inside a root, for example: $y = \sqrt x$ , $y = {^3}\sqrt{{x - 5}}$, $y = 2{^4}\sqrt{{3x - 8}} + 11$

• 2.
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.

• 3.
i) Describe the transformation(s) that should be applied to the graph of y= $y = \sqrt x$ 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)
$y = -2 \sqrt {\frac{x}{3}-1}+5$