1. 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 117 Announcements: No calculator sharing on tests. xy = f(x) -5-3 0 01 13 55 Objective: SWBAT determine if a relation has an inverse using the horizontal line test and determine the inverse graphically and algebraically.

2. Slide 1- 2 The Inverse Composition Rule Verifying that two functions are inverses of each other. Inverses (Opposite operations)

3. Slide 1- 3 Inverse Relation The ordered pair (a,b) is in a relation if and only if the pair (b,a) is in the inverse relation. xy = f(x) -5-3 0 01 13 55 Find the inverse relation for the given relation to the right. Graph these points on your Bell Ringer graph. xy =f -1 (x)

5. Slide 1- 5 The Inverse Reflection Principle The points (a,b) and (b,a) in the coordinate plane are 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?

6. Slide 1- 6 Horizontal Line Test The inverse of a relation is a function if and only if each horizontal line intersects the graph of the original relation in at most one point.

7. 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 117 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.

8. Slide 1- 8 Example Finding an Inverse Function Algebraically

9. Date: 11/2/11- Section: 1.4 Bell Ringer: Angioplasty Ex 5 pg 117. pg #21 Go 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 131-136 HW: Extra Credit (on separate sheet): a) pg 128 #24 b) 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.

10. Slide 1- 10 One-to-one function

11. Bell Ringer: Go over test Parking 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 x 2, x 3 HW: pg 128 #21; pg 139 #2-12 evens None assigned HW: Extra Credit (on separate sheet): a) pg 128 #24 b) 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