Date: 10/31/11- Section: 1.4

Bell Ringer: Using graph paper, graph the line y = x. Plot the following points on your graph.

HW Requests: pg 128 #11-14, 15, 17, 19, 58, 59, 60 HW Adjustment: Continue work from pg 128 #11-14, 15, 17, 19, 58, 59, 60 ADD pg 129 #39-42

Homework: pg 129 #40-56 evens, Read Ex. 5 pg 117Announcements: No calculator sharing on tests.

x y = f(x)-5 -3-3 00 11 35 5

Objective: SWBAT determine if a relation has an inverse using the horizontal line test and determine the inverse graphically and algebraically.

Slide 1- 2

The Inverse Composition Rule A function is one-to-one with inverse function if and only if

( ( )) for every in the domain of , and ( ( )) for every in the domain of .

f gf g x x x gg f x x x f

Verifying that two functions are inverses of each other.

Inverses (Opposite operations)

Slide 1- 3

Inverse Relation

The ordered pair (a,b) is in a relation if and onlyif the pair (b,a) is in the inverse relation.

x y = f(x)-5 -3-3 00 11 35 5

Find the inverse relation for the given relation to the right. Graph these points on your Bell Ringer graph.

x y =f-1(x)

Slide 1- 5

The Inverse Reflection Principle

The points (a,b) and (b,a) in the coordinate planeare symmetric with respect to the line y=x. The points (a,b) and (b,a) are reflections of each other across the line y=x.

What did you note about the inverse relation as you graphed it?

Slide 1- 6

Horizontal Line TestThe inverse of a relation is a function if and onlyif each horizontal line intersects the graph of theoriginal relation in at most one point.

Date: 11/1/11- Section: 1.4

Bell Ringer: What is a relation? What is a function?Describe the test we use to determine if a relation is a function? Describe the test we use to determine if function or relation has an inverse function.pg 128 #14, 15, 17, 19, 58, 59, 60

HW Requests: pg 128 #11-14, HW Adjustment: Continue work from pg 128 #11-14, 15, 17, 19, 58, 59, 60 ADD pg 129 #39-42

Homework: pg 129 #40-56 evens, Read Ex. 5 pg 117Announcements: No calculator sharing on tests.

Objective: SWBAT determine if a relation has an inverse using the horizontal line test and determine the inverse graphically and algebraically.

Slide 1- 8

Example Finding an Inverse Function Algebraically

-1 2Find an equation for ( ) if ( ) .

1xf x f x

x

-1

2 Switch the and 1

Solve for :( 1) 2 Multiply by 1

2 Distribute 2 Isolate the terms

( 2) Factor out

Divide by 22

Therefore ( ) .2

yx x yy

yx y y yxy x y xxy y x yy x x y

xy xx

xf xx

Date: 11/2/11- Section: 1.4

Bell Ringer: Angioplasty Ex 5 pg 117. pg #21Go over one-to-one functions

HW Requests: Get into same groups as yesterday (Group leaders) Compare answers on homework. Each group will put up a problem from Homework (pg 129 #40-56 evens,)

In class: Complete in class worksheet. Each person turns in a copy showing all work for full credit.

HW: pg 128-130 #22, 23, 68, 69, pg 139 Quick Review #2-10 evens; Read Section 1.5 pg 131-136HW: Extra Credit (on separate sheet): a) pg 128 #24b) The average of three numbers is 70. When the smallest of the three numbers is replaced by 75, the average is increased by 5. What is the number that was replaced by 75?

Announcements: No calculator sharing on tests.

Objective: SWBAT determine if a relation has an inverse using the horizontal line test and determine the inverse graphically and algebraically.

Slide 1- 10

One-to-one function

-1

-1

If is a one-to-one function with domain and range , then the , denoted , is the function with domain and range

defined by ( ) if and only if ( ) .

f D Rf R D

f b a f a b

inversefunction of f

Bell Ringer: Go over testParking Lot: Inherited domains from inverses

HW Requests: pg 128-130 #22, 23, 68, 69, pg 139 Quick Review #2-10 evens;

In class: Get into same groups as yesterday (Group leaders) Complete in class worksheet. Each person turns in a copy showing all work for full credit. Exploration 1 page 132 Functions x2, x3

HW: pg 128 #21; pg 139 #2-12 evens None assigned

HW: Extra Credit (on separate sheet): a) pg 128 #24b) The average of three numbers is 70. When the smallest of the three numbers is replaced by 75, the average is increased by 5. What is the number that was replaced by 75?Announcements: No calculator sharing on tests.

Date: 11/4/11 Section 1.4 Objective: SWBAT determine if a relation has an inverse using the horizontal line test and determine the inverse graphically and algebraically. Walton-page NUTALL, Page 1.2 Test