PreCalculus 12

1

2.1 Radical Functions A radical function is one that involves a radical with a ________________ in the radicand.

e.g. but not

The simplest radical function is ________________.

x y

Domain: Range:

The domain is restricted, as the __________________________________. We can use transformations to alter

the radical function into any general form: ( )y a b x h k � �

h

k

a

b

PreCalculus 12

2

Example: – Sketch the graphs, and give domain and range:

a) 3 3y x � � � b) ( ) 3 ( 1)f x x � �

c) 3 2y x� �

y x y x � 2y x � 3 2y x� �

PreCalculus 12

3

Example: - Determine the equation for the function:

vertical stretch or horizontal stretch

If we do not immediately recognize the stretch, we may substitute in an (x,y) point to find a parameter:

Example: Give the equation of:

PreCalculus 12

4

On your Own: Graph the function 𝑓(𝑥) = −(𝑥 + 2)2 + 1 and the function 𝑔(𝑥) = √𝑓(𝑥)

Example: Solve the following equation: √2𝑥 − 1 = 𝑥 − 4

Assignment: p. 89 # 1, 4-7, 8a

x y