Class Opener:. Identifying a Composite Function:

Slides:

Advertisements

Similar presentations

3.4 Inverse Functions & Relations

Advertisements

One-to-one and Inverse Functions

Graphs of Inverse Functions. Inverse Sine Function The horizontal line test shows that the sine function is not one-to-one and has no inverse function.

Inverse Functions Section 1.8.

Domains and Inverse Functions

4.1 Inverses Mon March 23 Do Now Solve for Y 1) 2)

Finding the Inverse. 1 st example, begin with your function f(x) = 3x – 7 replace f(x) with y y = 3x - 7 Interchange x and y to find the inverse x = 3y.

Functions Domain and range The domain of a function f(x) is the set of all possible x values. (the input values) The range of a function f(x) is the set.

DO NOW: 6.3: w/s C: Perform the indicated operation. 1.) Find g(f(x)) if f(x) = 2x 2 – x and g(x) = 2.) Find g(h(8)) if g(x) = -x 2 and h(x) =

Bellwork: Graph each line: 1. 3x – y = 6 2. Y = -1/2 x + 3 Y = -2

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

Warm Up I can use composition of functions to verify an inverse.

Math 71B 9.2 – Composite and Inverse Functions 1.

Pre-Calculus Chapter 1 Exam Review Look over your quizzes! Practice questions in your study plan!

Finding the Inverse.  If f(a) = b, then a function g(x) is an inverse of f if g(b) = a.  The inverse of f(x) is typically noted f -1 (x), which is read.

Inverse functions Calculus Inverse functions Switch x and y coordinates Switch domains and ranges Undo each other. Not all functions have an inverse,

Section 4.1 Inverse Functions. What are Inverse Operations? Inverse operations are operations that “undo” each other. Examples Addition and Subtraction.

Do Now: Find f(g(x)) and g(f(x)). f(x) = x + 4, g(x) = x f(x) = x + 4, g(x) = x

7.5 Inverses of Functions 7.5 Inverses of Functions Objectives: Find the inverse of a relation or function Determine whether the inverse of a function.

1.4 Building Functions from Functions

1 1.6: Inverse functions. Find the inverse of the function and algebraically verify they are inverses.

One-to-one and Inverse Functions 2015/16 Digital Lesson.

1.8 Inverse Functions. Any function can be represented by a set of ordered pairs. For example: f(x) = x + 5 → goes from the set A = {1, 2, 3, 4} to the.

Consider the function: Now, interchange the x- and y- coordinates in the set of ordered pairs above. This new set of ordered pairs is called the inverse.

Math – Exponential Functions

Ch 9 – Properties and Attributes of Functions 9.5 – Functions and their Inverses.

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)

Copyright © Cengage Learning. All rights reserved. 1 Functions and Their Graphs.

5.3 INVERSE FUNCTIONS OBJECTIVES VERIFY ONE FUNCTION IS THE INVERSE OF ANOTHER DETERMINE WHETHER A FUNCTION HAS AN INVERSE FIND THE DERIVATIVE OF AN INVERSE.

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.

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.

Functions 4 Reciprocal & Rational Functions

3.1 Functions x is called the independent variable

Quadratic and Square Root Inverse Relationships with Restrictions

Objectives: To find inverse functions graphically & algebraically.

Chapter 1: Lesson 1.9 Inverse Functions

a. Write a function, f(x), to represent the 5 bonus points.

2.6 Inverse Functions.

Inverse Functions Algebra III, Sec. 1.9 Objective

Functions and Their Graphs

JeopardySections Pre-Calculus designed by: Dunbar

Horizontal Line Test.

College Algebra Chapter 4 Exponential and Logarithmic Functions

4-5:One-to-One Functions and Their Inverses

Lesson 1.6 Inverse Functions

Operations on Functions, Compositions, and Inverses

Functions Review.

Sullivan Algebra and Trigonometry: Section 8.1

Inverse Functions Rita Korsunsky.

3-4 Inverse Functions and Relations

Ch 1.6: Inverse of Functions and Relations

Would be good homework on the inverse day!!!

1.9 Inverse Functions f-1(x) Inverse functions have symmetry

One-to-one and Inverse Functions

Notes Over 7.4 Finding an Inverse Relation

Chapter 5: Exponential and Logarithmic Functions

{(1, 1), (2, 4), (3, 9), (4, 16)} one-to-one

Inverse Trigonometric Functions

Sec. 2.7 Inverse Functions.

College Algebra Chapter 4 Exponential and Logarithmic Functions

Algebra 2/Trig Name:__________________________

One-to-one and Inverse Functions

One-to-one and Inverse Functions

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

7.4 Slope Objectives: To count slope To use slope formula.

Ch 8.8: Inverse of Functions and Relations

3.6 - Inverse Functions Notation: Say: “f-inverse of x”…

Do Now: Given f(x) = 2x + 8 and g(x) = 3x2 – 1 find the following.

FUNCTIONS & THEIR GRAPHS

Presentation transcript:

Class Opener:

Identifying a Composite Function:

Identifying a Composition of Two Functions:

ORQ Practice: Bacteria Count:

Inverse Functions:

Finding the Inverse Function Informally

Verifying the Inverse Function Algebraically

One – to – One Functions A function is one to one if, for a and b in its domain, f(a) = f(b) implies that a = b. A function f has an inverse function if and only if f is one to one.

Testing for one to one functions

Testing one to one functions

Horizontal Line Test Use the horizontal line test on a graph of a function to see if it is one to one. If it is a function the horizontal line will only hit the function one time.