Name: ____________________ Pre- Calculus 12 H Date: _____________

Chapter 2– Radical Functions Section 2.1 - Radical Functions and Transformations

Specific Outcome: Students will graph and analyze radical functions (limited to functions involving

one radical).

investigating the function y x using a table of values and a graph

graphing radical functions using transformations

identifying the domain and range of radical functions

Let’s review the basic radical function: Radical Function (a.k.a. square root function)

y x

____________________

Domain:

Range:

Examples of Radical Transformations:

2y x

___

Domain:

Range:

Mapping: (x, y)

2 3y x

Domain:

Range:

Mapping: (x, y)

Name: ____________________ Pre- Calculus 12 H . Date: _____________

Chapter 2– Radical Functions Section 2.2 – Square Roots of a Function

Focus on . . . sketching the graph of ( )y f x given the graph of y = f (x)

explaining strategies for graphing ( )y f x given the graph of y = f (x)

comparing the domains and ranges of the functions y = f (x) and ( )y f x and explaining any differences

Radical function: A radical function has the form ( )y f x , where ( )f x is a function. The square root of

a function is only defined for non-negative numbers, so the domain of ( )y f x is the set of values of x for

which ( ) 0f x

( )y f x vs. ( )y f x

1) Consider the functions 1 2 1y x & 2 2 1y x

Describe in words what is happening mathematically with these two functions. Graph the two

functions

y = 2x + 1 ______________________________________________________________________.

2 1y x ______________________________________________________________________.

x 1 2 1y x

2 2 1y x

0

4

12

24

40

2) Compare Graphically:

2 1y x D:

R:

2 1y x D:

R:

( )y f x ( )y f x : This is a ____________________ transformation.

Mapping: ( , y) x

Five facts concerning square roots:

1. The square root of a negative number is undefined.

2. The square root of zero is zero.

3. The square root of a number is larger than the number when the number is between zero and one.

4. The square root of one is one.

5. The square root of a number is smaller than the number for numbers larger than one.

Relative Locations of ( )y f x and ( )y f x

Observe the graph above. What can we predict about ( )y f x when ( )y f x is in a relative location?

Value of

f(x)

( ) 0f x ( ) 0f x 0 ( ) 1f x ( ) 1f x ( ) 1f x

Relative

Location of

Graph of

( )y f x

Compare the Domains of ( )y f x and ( )y f x

Example: Identify and compare the domains and ranges

of 22 0.5y x and

22 0.5y x .

Function 22 0.5y x 22 0.5y x

x-intercepts

y-intercepts

Maximum Value

Minimum Value

Graph ( )y f x from ( )y f x :

Example: 4y x

Example: 20.5 1y x

Example: State the coordinates of any invariant points when f (x) 1

2x 3 is transformed to y f (x)

Example: If (3, 18) is a point on the graph of ( )y f x , identify one point from 2 ( 3)y f x .

Assignment 2.1: p. 72 #2-4, 9a, 10, 11, 16 Assignment 2.2: p. 86 #1-3, 8a, 11, 16, 17ac