6.5 - Graphing Square Root and Cube Root Functions

Ex 1: Graph ( )f x x

0149

x y

0123

Domain of f(x) ? _____________________Range of f(x)? _____________________For square root functions, is the _____________ function.

{ 0}x x{ 0}y y

parent( )f x x

Ex 2: Graph ( ) 3g x x

( ) 3g x x ( )f x x

Transformations:

Domain of g(x)? ___________

Range of g(x)? ___________

{ 3}x x

{ 0}y y

Right 3

Ex 3: Graph

( )f x x

Transformations:

Domain of h(x)? __________

Range of h(x)? __________

{ 0}x x

{ 3}y y

up 3

1/2( ) 3h x x 1/2( ) 3h x x

Graph

Transformations:

Domain of f(x)? __________

Range of f(x)? __________

{ 5}x x

{ 2}y y

Down 2, left 5

( ) 5 2f x x

( ) 5 2f x x

Graph

Transformations:

Domain of g(x)? __________

Range of g(x)? __________

{ 2}x x

{ 4}y y

Down 4, left 2, reflect in x-axis

g x x 2 4

g x x 2 4

Graph

Transformations:

Domain of h(x)? _________

Range of h(x)? _________

{ 3}x x

{ 1}y y

Up 1, right 3, reflect in x-axis

1/2( ) 3 1h x x

1/2( ) 3 1h x x

f x x

Given the form , describe how a, h and k affect the shifting of

______________________________________

______________________________________

g x a x h k

When a is negative, reflect x axis

h: Left or right h: Up or Down

Starting point:(h, k)

Graph 3( )f x x

–8–1 0 1 8

x y

–2–1012

Domain of f(x) ? _____________________Range of f(x)? _____________________For square root functions, is the _____________ function.

{ }x x{ }y y

parent3( )f x x

Ex 5: Graph

( )f x x

Transformations:

Domain of g(x)? ___________

Range of g(x)? ___________

left 2, up 3

3( ) 2 3g x x

3( ) 2 3g x x

{ }x x

{ }y y

Graph

Transformations:

Domain of f(x)? __________

Range of f(x)? __________

Up 2, reflect in x-axis

{ }x x

{ }y y

1/3( ) 2f x x 1/3( ) 2f x x

Graph

Transformations:

Domain of g(x)? __________

Range of g(x)? __________

Right 4, reflect in x-axis

{ }x x

{ }y y

g x x 43

g x x 43

3( ) 2 1g x x Graph

Transformations:

Domain of g(x)? __________

Range of g(x)? __________

Right 2, down 1

{ }x x

{ }y y

3( ) 2 1g x x

Given the form , describe how a, h and k affect the shifting of

______________________________________

______________________________________

3g x a x h k

When a is negative, reflect x axis

h: Left or right h: Up or Down

Starting point:(h, k)

3f x x