Students, Take out your calendar and your homework

Slides:



Advertisements
Similar presentations
1.6 Functions. Chapter 1, section 6 Functions notation: f: A B x in A, y in B, f(x) = y. concepts: –domain of f, –codomain of f, –range of f, –f maps.
Advertisements

A set of ordered pairs is called a __________.
One-to-one and Inverse Functions
COORDINATE PLANE x-axisy-axis. COORDINATE PLANE QUADRANTS III III IV (+, +)(-, +) (-, -)(+, -)
4-3 Relations Objective: Students will represent relations as sets of ordered pairs, tables, mappings, and graphs. Students will find the inverse of a.
5-2 Relations Objective: To identify the domain, range, and inverse of a function and to show relations as sets of ordered pairs, tables, mappings, and.
Inverses Algebraically 2 Objectives I can find the inverse of a relation algebraically.
Pre-AP Pre-Calculus Chapter 1, Section 5 Parametric Relations and Inverses
Section 5.2 One-to-One Functions; Inverse Functions.
Math 71B 9.2 – Composite and Inverse Functions 1.
9.2 Relations CORD Math Mrs. Spitz Fall Objectives Identify the domain, range and inverse of a relation, and Show relations as sets of ordered pairs.
Notes Over 2.3 The Graph of a Function Finding the Domain and Range of a Function. 1.Use the graph of the function f to find the domain of f. 2.Find the.
Inverse Functions.
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.
Trig/Pre-Calculus Opening Activity
Chapter 7 – Radical Equations and Inequalities 7.2 – Inverse Functions and Relations.
One-to-one and Inverse Functions 2015/16 Digital Lesson.
Section 2.6 Inverse Functions. Definition: Inverse The inverse of an invertible function f is the function f (read “f inverse”) where the ordered pairs.
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.
Math – Exponential Functions
Inverse Functions Objective: To find and identify inverse functions.
Copyright © Cengage Learning. All rights reserved. 1 Functions and Their Graphs.
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.
Chapter 1 Functions and Their Graphs. Copyright © Houghton Mifflin Company. All rights reserved.1 | 2 Section 1.1, Slope of a Line.
TOPIC 20.2 Composite and Inverse Functions
Today in Pre-Calculus Do not need a calculator Review Chapter 1
Functions and Their Graphs
Properties of Functions
Section 3.3 – Rates of Change and Behavior of Graphs
Aim #2.2 What else is there to know about Functions and Their Graphs?
Inverse functions and Relations
Inverse Functions.
Find the Inverse and Graph the Functions
Chapter 6: Radical functions and rational exponents
Introduction to Functions
FUNCTIONS: A REVIEW ASSESSMENT QUESTIONS.
Evaluate each expression. Hint: Use the unit circle.
Warmup Let f(x) = x – 3 and g(x) = x2. What is (f ○ g)(1)?
Precalculus Day 36.
Lesson 1.6 Inverse Functions
Warmup: Find the inverse function for each:
Section 2.2 More on Functions and Their Graphs
Find the Inverse and Graph the Functions
Inverse Functions.
Ch 1.6: Inverse of Functions and Relations
Write each using Interval Notation. Write the domain of each function.
Students, Take out your calendar and your homework
One-to-one and Inverse Functions
One-to-One Functions;
Find the period and amplitude. Describe the shift.
Students, Take out your calendar and your homework
One-to-one and Inverse Functions
One-to-one and Inverse Functions
Inverse Relations and Functions.
1.6 - Relations.
3-1 Relations A relation is a set of points.
3.6 - Inverse Functions Notation: Say: “f-inverse of x”…
Algebra 1 ~ Chapter 4.1 The Coordinate Plane.
Divide. Use synthetic division.
Students, Take out your calendar and your homework
Find all the zeros of the functions.
Find all the solutions without using a calculator.
L8-3 Obj: Students will use definition of log
Graphing Horizontal and
Students, Take out your calendar and your homework
Evaluate each expression. Hint: Use the unit circle.
Students, Take out your calendar and your homework
Multiply each expression.
Packet #12 Composite, One-to-one, and Inverse Functions
2-1 Relations & Functions
Presentation transcript:

Students, Take out your calendar and your homework Students, Take out your calendar and your homework. Take out your spiral notebook and Complete the DNA. Use your notes if necessary.

Inverse Functions Functions can be written as a set of ordered pairs. If we reverse the order of the coordinates (switch them) we obtain the inverse function of f:

Existence of an Inverse A function has an inverse if and only if it is one-to-one. This means that no two elements in the domain of a function correspond to the same element in the range. To test for an inverse (does one exist), use the horizontal line test.

Find the inverse function of Example 6 Find the inverse function of .

Graph each function on your graphing calculator Graph each function on your graphing calculator. Describe the difference between each. Which is the parent function?

Find the domain of the functions.

Determine the relative minima and maxima of the following function Determine the relative minima and maxima of the following function. Determine where the graph is increasing, decreasing, and constant.

Compositions of Functions