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.

Slides:

Advertisements

Similar presentations

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.

Advertisements

Inverse Functions Section 1.8.

Objective Video Example by Mrs. G Give It a Try Lesson 7.4  Identify and graph parent functions of the following families of functions: Linear Absolute.

Domains and Inverse Functions

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

One-to One Functions Inverse Functions

Prerequisite Skills VOCABULARY CHECK 1. The domain of the function is ?. 2. The range of the function is ?. 3. The inverse of the function is ?. ANSWER.

Functions A function is a relationship between two sets: the domain (input) and the range (output) DomainRange Input Output This.

Logarithmic Functions and Models Lesson 5.4. A New Function Consider the exponential function y = 10 x Based on that function, declare a new function.

Section 8.2 Inverse Functions

FIND THE DOMAIN AND RANGE OF THE FUNCTION: 1. FIND THE INVERSE OF THE FUNCTION. STATE ANY DOMAIN RESTRICTIONS. 2.

Graphs of Functions and Inverses What is the connection between the graphs of functions and their inverses?

Math-3 Lesson 4-1 Inverse Functions. Definition A function is a set of ordered pairs with no two first elements alike. – f(x) = { (x,y) : (3, 2), (1,

Functions Review.

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) =

CA STANDARDS 20.0: Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations. Agenda 1.) Lesson.

What is the symmetry? f(x)= x 3 –x.

A Library of Parent Functions. The Constant Parent Function Equation: f(x) = c Domain: (-∞,∞) Range: [c] Increasing: None Decreasing: None Constant: (-∞,∞)

Section 4.7 – The Quadratic Formula Students will be able to: To solve equations using the Quadratic Formula To determine the number of solutions by using.

Lesson 5.3 Inverse Functions

Domain and Range Restriction Pt What are the different symbols that you use when writing domain and range restrictions? Write your answer in a.

Topic #2: Understanding Inverse Relations

Section Day 2 Solving Trig Equations Using Inverses.

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

Inverse Functions.

Lesson 1.6 Inverse Functions. Inverse Function, f -1 (x): Domain consists of the range of the original function Range consists of the domain of the original.

3.1 Derivative of a Function Objectives Students will be able to: 1)Calculate slopes and derivatives using the definition of the derivative 2)Graph f’

Graphing Log Functions Pre-Calculus. Graphing Logarithms Objectives:  Make connections between log functions and exponential functions  Construct a.

Find the inverse of a power function

Calculating Algebraic Inverses. Daily Check Find the inverse of the following functions.

MAT 150 Module 7 – Operations with Functions Lesson 3 – Inverse Functions ons/1/11/Inverse_Function_Graph.png.

Inverse functions: if f is one-to-one function with domain X and range Y and g is function with domain Y and range X then g is the inverse function of.

6.4 Notes – Use Inverse Functions. Inverse: Flips the domain and range values Reflects the graph in y = x line. Functions f and g are inverses of each.

CHAPTER 10 LESSON OBJECTIVES. Objectives 10.1 Students will be able to: Identify quadratic functions and determine whether they have a minimum or maximum.

2.2 day 3 The Piecewise Function

Lesson 1.6 Page 69: #1-77 (EOO) EXTRA CREDIT: Pages (Do any 20 problems…You choose )

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.

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

How do I find the inverse of functions? 4.3 Use Inverse Functions Inverse Functions Functions f and g are inverse functions of each other provided: The.

Functions LINEAR AND NON LINEAR. Linear function What is the function that states that the range values are 2 more than the domain values?  f(x) = 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.

1 Lecture 7 of 12 Inverse Trigonometric Functions.

Parent Functions. Learning Goal I will be able to recognize parent functions, graphs, and their characteristics.

Quadratic and Square Root Inverse Relationships with Restrictions

Piecewise Functions At least 2 equations, each of which applies to a different part of the functions domain. It is like having 3 equations for 3 different.

Warm Up Identify the domain and range of each function.

Objective 1A f(x) = 2x + 3 What is the Range of the function

Piecewise Functions At least 2 equations, each of which applies to a different part of the functions domain. It is like having 3 equations for 3 different.

Relations and Function

3.3 The Inverse of a Quadratic Function

Inverse Functions.

Graphing and Evaluating The Piecewise Function A Series of Examples

Drawing Quadratic Graphs

Objectives The student will be able to:

Inverse Functions Inverse Functions.

1.6 - Relations.

Quadratic graphs.

Drawing Graphs The straight line Example

Warm Up #8 Sketch the graphs of: 1.

L8-3 Obj: Students will use definition of log

Find the inverse of a power function

Review: How do you find the inverse of a function? Application of what you know… What is the inverse of f(x) = 3x? y = 3x x = 3y y = log3x f-1(x) = log3x.

Graphing Quadratic Functions

Objectives The student will be able to:

LINEAR & QUADRATIC GRAPHS

Bell ringer f(x) = 15x – 1 2. f(x) = 1 3 x + 7

2.1(b) Notes: Graphing Quadratic Functions

Presentation transcript:

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 between the domains and ranges of a function and its inverse. To know when it is possible to find an inverse function. (quadratics!) Functions Lesson 4

Finding inverse functions Recap We can find the inverse of a one-to-one function f ( x ) by ? Find the inverse of for -3 < x < 3 So the inverse function in terms of x is

Inverse functions How are the graphs of f ( x ) and f –1 ( x ) related? Domain is: -3 < x < 3 Range is: < y < Domain is: < x < Range is: < y < So the domain of f(x) is the _________________ of f -1 (x) And the range of f(x) is the _________________ of f -1 (x)

Try w/s

Quadratics Draw y = x 2 Why is this not a function? We can make it a function by restricting the domain to? What is the inverse? Draw it!

Finding inverse functions When finding the inverse of a general quadratics, we need to complete the square in order to find the solution. Find the inverse of,. Note the range of f(x) is y > So the domain of f -1 (x) will be x >

Try These