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Review: Given Find Looking Ahead – Challenge: Graph the points: A (-2,-3) B (-1,1) C (3,5) Connect the points from A to B to C. Math 93: Kathy Conway Instructor

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§ 8.4 Composite and Inverse Functions 1.Form Composite Functions 2.Verify Inverse Functions 3.Find the Inverse 4.Horizontal Line Test 5.Graphs of Inverse Functions

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Blitzer, Introductory and Intermediate Algebra, 3e – Slide #3 Section 8.4 Graphs of Inverse Functions f(x) xy A -24 B 0 C 51

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Blitzer, Introductory and Intermediate Algebra, 3e – Slide #4 Section 8.4 Graphs of Inverse Functions f(x) xy A -24 B 0 C 51 f -1 (x) xy A 4-2 B 0 C 15

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Blitzer, Introductory and Intermediate Algebra, 3e – Slide #5 Section 8.4 Graphs of Inverse Functions

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Blitzer, Introductory and Intermediate Algebra, 3e – Slide #6 Section 8.4 Graphs of Inverse Functions

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Blitzer, Introductory and Intermediate Algebra, 3e – Slide #7 Section 8.4 Graphs of Inverse Functions Review: y = f(x) is a function if it passes the vertical line test.vertical line test The inverse of f(x) is a function if it passes the horizontal line test.horizontal line test New: It is a One-to-One (1-1) function if it passes both the vertical line test and the horizontal line test.horizontal line test A 1-1 function is a function in which no two different ordered pairs have the same second component. Only 1-1 functions have inverse functions.

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Blitzer, Introductory and Intermediate Algebra, 3e – Slide #8 Section 8.4 Inverse Functions Graphs of f and T There is a relationship between the graph of a one-to-one function, f, and its inverse,. Because inverse functions have ordered pairs with the coordinates reversed, if the point (a,b) is on the graph of f, then the point (b,a) is on the graph of. The points (a,b) and (b,a) are symmetric with respect to the line y = x. Thus, the graph of is a reflection of the graph of f about the line y = x.

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Blitzer, Introductory and Intermediate Algebra, 3e – Slide #9 Section 8.4 Some reminders… Note that: means f inverse and not f to the negative one power

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Blitzer, Introductory and Intermediate Algebra, 3e – Slide #10 Section 8.4 Inverse & Horizontal Line Test Assignment: 1.Math Lab Plus = My Math Lab (MML): 8.4 #1-24 Due Thursday, October 18 at beginning of class 2.Homework 8.4 #2, 6, 16, 18, 26, 30, 32, 38, 42, 48 I will give you the answers tomorrow and we will discuss questions so bring completed homework tomorrow, but Due Thursday, October 18 at beginning of class

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PRECALCULUS Inverse Relations and Functions. If two relations or functions are inverses, one relation contains the point (x, y) and the other relation.

PRECALCULUS Inverse Relations and Functions. If two relations or functions are inverses, one relation contains the point (x, y) and the other relation.

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