name: pre- calculus 12 h chapter 2 radical functions...
TRANSCRIPT
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