1. Unit 1: Functions Minds On What do you think of when you hear “inverse”?

2. Unit 1: Functions Minds On a) Graph: f(x) = (x – 2) 2 - 1 and determine the domain and range b) Graph the inverse by switching all the (x, y) coordinates. Determine the domain and range of the inverse.

3. Unit 1: Functions Lesson 5: Inverse Functions Learning Goal: I can determine the inverse of a function and its algebraic expression, set of values (ordered pairs) as it relates to the original function.

4. Unit 1: Functions Lesson 5: Inverse Functions

5. Unit 1: Functions Lesson 5: Inverse Functions Properties of the Inverse of a Function If (a, b) is a point on the graph of y = f(x), then (b, a) is a point on the graph of y = f -1 (x) The domain of f(x) will be the range of f -1 (x) The range of f(x) will be the domain of f -1 (x) The graph of y = f -1 (x) is the reflection of y = f(x) in the line y = x

6. Unit 1: Functions Lesson 5: Inverse Functions

7. Unit 1: Functions Lesson 5: Inverse Functions i. graph the relationship and state domain and range D= R = Given the relation {(-2,3), (0,4), (2,5), (3,4), (5,2), (6,l)} ii. switch the x and y coordinates to graph the inverse relationship and state the domain and range D= R = iii. Graph the line y = x. Compare the points on the original function and their corresponding points on the inverse. What do you notice?

8. Unit 1: Functions Lesson 5: Inverse Functions How do we determine the inverse of a function? 1) Replace f(x) with y f(x) = 3x - 5 becomesy = 3x - 5 2) Switch x and y in the equation. y = 3x - 5becomesx = 3y - 5

9. Unit 1: Functions Lesson 5: Inverse Functions

10. Unit 1: Functions Lesson 5: Inverse Functions Example: Find the inverse of f(x) = x + 2

11. Unit 1: Functions Lesson 5: Inverse Functions Example: Find the inverse of f(x) = 2x

12. Unit 1: Functions Lesson 5: Inverse Functions

13. Unit 1: Functions Lesson 5: Inverse Functions Given the function h(x) = 2x – 4, determine h -1 (-3)

14. Unit 1: Functions Lesson 5: Inverse Functions Example: Find the inverse of f(x) = (x – 3) 2 + 5

15. Unit 1: Functions Lesson 5: Inverse Functions The inverse of a quadratic is NOT a function. We can make it a function by restricting the domain.

16. Unit 1: Functions Lesson 5: Inverse Functions NEW Homework  Pg. 46-49 #1a, 2bd, 4, 6, 8, 9a-e, 10ace, 15  Pg. 160-162 #1a, 2b, 3, 4, 10  Extra: Level 4 Pg. 46-49 #16, 17 Pg. 160-162 #13