Inverse Function Recap. Determine whether these functions are one-to-one. Problems 10 and 12 from red book.

Slides:



Advertisements
Similar presentations
6.7 Notes – Inverse Functions. Notice how the x-y values are reversed for the original function and the reflected functions.
Advertisements

6.2 One-to-One Functions; Inverse Functions
Inverse Functions. Objectives  Students will be able to find inverse functions and verify that two functions are inverse functions of each other.  Students.
Inverse Functions Section 1.8.
Operations on Functions Composite Function:Combining a function within another function. Written as follows: Operations Notation: Sum: Difference: Product:
7.4 Inverse Functions p Review from chapter 2 Relation – a mapping of input values (x-values) onto output values (y-values). Here are 3 ways to.
Domains and Inverse Functions
Miss Battaglia AP Calculus. A function g is the inverse function of the function f if f(g(x))=x for each x in the domain of g and g(f(x))=x for each x.
One-to One Functions Inverse Functions
Sullivan PreCalculus Section 4.2 Inverse Functions
5.2 Inverse Function 2/22/2013.
Inverse Functions By Dr. Carol A. Marinas. A function is a relation when each x-value is paired with only 1 y-value. (Vertical Line Test) A function f.
Operations with Functions Section 2.4.  Sum  Difference  Product  Quotient  Composition Types of Operations.
Copyright © 2009 Pearson Education, Inc. CHAPTER 5: Exponential and Logarithmic Functions 5.1 Inverse Functions 5.2 Exponential Functions and Graphs 5.3.
Slide Copyright © 2009 Pearson Education, Inc.
INVERSE FUNCTIONS Section 3.3. Set X Set Y Remember we talked about functions--- taking a set X and mapping into a Set Y An inverse.
Do Now: Plot the following coordinates in a coordinate plane: HW: Page ,68,69,70.
Today in Pre-Calculus Go over homework questions Notes: Inverse functions Homework.
Combinations of Functions & Inverse Functions Obj: Be able to work with combinations/compositions of functions. Be able to find inverse functions. TS:
Inverse Functions Given 2 functions, f(x) & g(x), if f(g(x))=x AND g(f(x))=x, then f(x) & g(x) are inverses of each other. Symbols: f -1(x) means “f.
INVERSE FUNCTIONS. Set X Set Y Remember we talked about functions--- taking a set X and mapping into a Set Y An inverse function.
CHAPTER 6 SECTION 6 : FUNCTIONS AND THEIR INVERSES.
3.4 Use Inverse Functions p. 190 What is an inverse relation?
More Quarter test review Section 4.1 Composite Functions.
7.8 Inverse Functions and Relations Horizontal line Test.
4.1 – ONE-TO-ONE FUNCTIONS; INVERSE FUNCTIONS Target Goals: 1.Obtain the graph of the inverse function 2.Determine the inverse of a function.
1.8 Inverse Functions, page 222
1.4 Building Functions from Functions
Quick Crisp Review Graphing a piecewise function Determine relative max and min Graphing a step function 35)a) oddb) even (-3/2, 4)
1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-1 Exponential and Logarithmic Functions Chapter 9.
Chapter 7 – Radical Equations and Inequalities 7.2 – Inverse Functions and Relations.
1 1.6: Inverse functions. Find the inverse of the function and algebraically verify they are inverses.
Review Relation – a mapping of input values (x-values) onto output values (y-values). Here are 3 ways to show the same relation. y = x 2 x y
Aims: To be able to find the inverse of a function. To know the graphical relationship between a function and its inverse. To understand the relationship.
Copyright © 2011 Pearson Education, Inc. Inverse Functions Section 2.5 Functions and Graphs.
6.2 Inverse functions and Relations 1. 2 Recall that a relation is a set of ordered pairs. The inverse relation is the set of ordered pairs obtained by.
7.4 Inverse Functions p. 422 What is an inverse relation? What do you switch to find an inverse relation? What notation is used for an inverse function?
OBJECTIVES:  Find inverse functions and verify that two functions are inverse functions of each other.  Use graphs of functions to determine whether.
Ch 9 – Properties and Attributes of Functions 9.5 – Functions and their Inverses.
Inverse Functions. Definition A function is a set of ordered pairs with no two first elements alike. f(x) = { (x,y) : (3, 2), (1, 4), (7, 6), (9,12) }
Inverse Functions Objective: To find and identify inverse functions.
Do Now: Given f(x) = 2x + 8 and g(x) = 3x 2 – 1 find the following. 1.) (f + g)(x) 2.) g(x – 2)
5.3 Inverse Functions (Part I). Objectives Verify that one function is the inverse function of another function. Determine whether a function has an inverse.
Objective: Find inverse functions. Warm up 1. a.Find (f o g)(x). b.Find the domain of f(g(x)).
Inverse Functions Pages in Text Any Relevant Graphics or Videos.
Objectives: 1)Students will be able to find the inverse of a function or relation. 2)Students will be able to determine whether two functions or relations.
Inverse Functions. DEFINITION Two relations are inverses if and only if when one relation contains (a,b), the other relation contains (b,a).
1. Warm-Up 4/15 F 5. Rigor: You will learn how to find inverse functions algebraically and graphically. Relevance: You will be able to use functions.
5.3- Inverse Functions If for all values of x in the domains of f and g, then f and g are inverse functions.
2.6 Inverse Functions.
Welcome! September 18, 2017 Graph paper/Calculator 1.4 HW Quiz Warm-up
Warmup Let f(x) = x – 3 and g(x) = x2. What is (f ○ g)(1)?
Inverse Relations & Square Root Functions
Relations.
Chapter 3 – The Nature of Graphs
Section 1.6 Transformation of Functions
Inverse Functions.
Attributes and Transformations of Reciprocal Functions
solution set (describes all values that make an equation true.)
Relations for functions.
6.4 Use Inverse Functions.
3 Inverse Functions.
Objectives The student will be able to:
{(1, 1), (2, 4), (3, 9), (4, 16)} one-to-one
Sec. 2.7 Inverse Functions.
Algebra 2/Trig Name:__________________________
7.4 Inverse Functions p. 422.
TI-83: y = , 2nd x2 , 49 – x^2 to get Then hit graph Range [0, 7]
7.4 Inverse Functions.
Objectives The student will be able to:
Presentation transcript:

Inverse Function Recap

Determine whether these functions are one-to-one. Problems 10 and 12 from red book

Determine whether the function is one-to- one. {(-2, 5), (-1, 3), (3, 7), (4, 12)}

Given the graph of f, use the horizontal line test to determine whether f is one-to- one

The graph of a one-to-one function f is given. Draw the graph of the inverse function f -1.

Verify that the functions f and g are inverses of each other by showing that f(g(x))=x and g(f(x))=x. Give any values of x that need to be excluded. f(x)=3-2x; g(x)=-1/2(x-3)

The function f is one-to-one. Find its inverse and check your answer. Sate the domain and the range of f and f -1. Graph f, f -1, and y=x on the same coordinate axes. f(x)=x 3 +1

Assignment Due Tuesday Transformations Worksheet Textbook Pages Problems 7(all parts), 9(parts a-d only), and 11(parts a and b only) RED BOOK Pages Problems 9-21odd, 31-39odd, and odd QUIZ OVER INVERSE FUNCTIONS TUESDAY