Chapter 7.8 Inverse Functions and Relations Standard & Honors

Slides:



Advertisements
Similar presentations
Operations on Functions Composite Function:Combining a function within another function. Written as follows: Operations Notation: Sum: Difference: Product:
Advertisements

Inverses Algebraically 2 Objectives I can find the inverse of a relation algebraically.
Copyright © 2011 Pearson, Inc. 1.5 Parametric Relations and Inverses.
Splash Screen. Lesson Menu Five-Minute Check (over Lesson 6–1) CCSS Then/Now New Vocabulary Key Concept: Inverse Relations Example 1:Find an Inverse Relation.
Name:__________ warm-up 6-2 Using f(x) = 3x + 2 and g(x) = 2x 2 – 1, find (f – g)(x), if it exists. Using f(x) = 3x + 2 and g(x) = 2x 2 – 1, find (f ●
Transparency 3 Click the mouse button or press the Space Bar to display the answers.
SAT Problem of the Day. 2.5 Inverses of Functions 2.5 Inverses of Functions Objectives: Find the inverse of a relation or function Determine whether the.
Transparency 2 Click the mouse button or press the Space Bar to display the answers.
Lesson 5-2 Slope and Direct Variation. Transparency 2 Click the mouse button or press the Space Bar to display the answers.
Unit 1: Functions Minds On What do you think of when you hear “inverse”?
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.
Transparency 3 Click the mouse button or press the Space Bar to display the answers.
Chapter 7 – Radical Equations and Inequalities 7.2 – Inverse Functions and Relations.
Transparency 2 Click the mouse button or press the Space Bar to display the answers.
3.2 Inverse Functions. Functions A function maps each element in the domain to exactly 1 element in the range.
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.
Lesson 4-6 Relations. Transparency 6 Click the mouse button or press the Space Bar to display the answers.
Inverse Relations and Functions
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.
7-8: Inverse Functions and Relations. Terms to Know Inverse relation: the set of ordered pairs obtained by reversing the coordinates of each original.
Click the mouse button or press the Space Bar to display the answers.
Click the mouse button or press the Space Bar to display the answers.
2.6 Inverse Functions.
Inverse Functions Algebra III, Sec. 1.9 Objective
Find the Inverse and Graph the Functions
Algebra II Mr. Gilbert Chapter 2.5 Modeling Real-World Data:
Chapter 10.1 Exponential Functions Standard & Honors
Chapter 5.8 Radical Equations & Inequalities Standard & Honors
Chapter 7.6 Rational Zero Theorem Standard & Honors
Chapter 7.4 The Remainder and Factor Theorems Standard & Honors
Warmup Let f(x) = x – 3 and g(x) = x2. What is (f ○ g)(1)?
INVERSE Functions and their GRAPHS
Inverse Functions 5.3 Chapter 5 Functions 5.3.1
Lesson 1.6 Inverse Functions
Splash Screen.
Chapter 6.2 Solving Quadratic Functions by Graphing Standard & Honors
Chapter 6.6 Analyzing Graphs of Quadratic Functions Standard & Honors
Chapter 6.4 Completing the Square Standard & Honors
Chapter 10.6 Exponentials Growth and Decay Standard & Honors
Chapter 10.2 Logarithms and Logarithmic Functions Standard & Honors
Graphing and Solving Quadratic Inequalities
Chapter 6.3 Solving Quadratic Functions by Factoring Standard & Honors
Review Chapter 6 Standard & Honors
Chapter 10.5 Base e and Natural Logarithms Standard & Honors
Review Chapter 7.7, 7.8 &11.7 Standard & Honors
Find the Inverse and Graph the Functions
Chapter 5.6: Radical Expressions Standard & Honors
The Quadratic Formula and the Discriminant
Splash Screen.
Solving Equations using Quadratic Techniques
Standards: MM2A5 – Students will explore inverses of functions.
Ch 1.6: Inverse of Functions and Relations
Click the mouse button or press the Space Bar to display the answers.
One-to-one and Inverse Functions
Geometry: Parallel and Perpendicular Lines
Section 1.8 INVERSE FUNCTIONS.
Honors Algebra II with Trigonometry Mr. Agnew
Writing Equations in Slope-Intercept Form
Sec. 2.7 Inverse Functions.
Algebra 2/Trig Name:__________________________
One-to-one and Inverse Functions
One-to-one and Inverse Functions
Inverse Relations and Functions.
Chapter 7.7 Operations on Functions Standard & Honors
Splash Screen.
Transformations on the Coordinate Plane
Inverse Functions   A function and its inverse function can be described as the "DO" and the "UNDO" functions.  A function takes a starting value, performs.
Chapter 10.3 Properties of Logarithms Standard & Honors
Reflections on the Coordinate Plane
Presentation transcript:

Chapter 7.8 Inverse Functions and Relations Standard & Honors Algebra II Mr. Gilbert Chapter 7.8 Inverse Functions and Relations Standard & Honors 11/29/2018

Agenda Warm up Homework Review Lesson Homework 7.7 Operations on Functions Lesson Homework 11/29/2018

Click the mouse button or press the Space Bar to display the answers. 11/29/2018 Click the mouse button or press the Space Bar to display the answers. Transparency 8

11/29/2018 Transparency 8a

Homework Review 11/29/2018

Communicate Effectively Domain & Range Inverse Relation : see below Inverse Function : f(x), f-1(x) Identity Function I(x)=x Two relations in an inverse if and only if whenever one contains (a,b) then the other contains (b,a). {this means all elements are included} 11/29/2018

7.8 Inverse Functions and Relations Example 1 Find an Inverse Relation (3) Example 2 Find an Inverse Function (5) Example 3 Verify Two Functions are Inverses (3) 11/29/2018 Lesson 8 Contents

Geometry The ordered pairs of the relation {(1, 3), (6, 3), (6, 0), (1, 0)} are the coordinates of the vertices of a rectangle. Find the inverse of this relation and determine whether the resulting ordered pairs are also the coordinates of the vertices of a rectangle. To find the inverse of this relation, reverse the coordinates of the ordered pairs. The inverse of the relation is {(3, 1), (3, 6), (0, 6), (0, 1)}. 11/29/2018 Example 8-1a

Answer: Plotting the points shows that the ordered pairs also describe the vertices of a rectangle. Notice that the graph of the relation and the inverse are reflections over the graph of y = x. 11/29/2018 Example 8-1b

Geometry The ordered pairs of the relation {(–3, 4), (–1, 5), (2, 3), (1, 1), (–2, 1)} are the coordinates of the vertices of a pentagon. Find the inverse of this relation and determine whether the resulting ordered pairs are also the coordinates of the vertices of a pentagon. Answer: {(4, –3), (5, –1), (3, 2), (1, 1), (1, –2)} These ordered pairs also describe the vertices of a pentagon. 11/29/2018 Example 8-1c

Step 1 Replace f (x) with y in the original equation. Find the inverse of Step 1 Replace f (x) with y in the original equation. Step 2 Interchange x and y. 11/29/2018 Example 8-2a

Step 4 Replace y with f –1(x). Step 3 Solve for y. Inverse Multiply each side by –2. Add 2 to each side. Step 4 Replace y with f –1(x). Answer: The inverse of is 11/29/2018 Example 8-2b

Graph the function and its inverse. Graph both functions on the coordinate plane. The graph of is the reflection for over the line 11/29/2018 Example 8-2d

Answer: 11/29/2018 Example 8-2e

b. Graph the function and its inverse. Answer: a. Find the inverse of b. Graph the function and its inverse. Answer: Answer: 11/29/2018 Example 8-2f

Determine whether and are inverse functions. Check to see if the compositions of f (x) and g (x) are identity functions. 11/29/2018 Example 8-3a

Answer: The functions are inverses since both and equal x. 11/29/2018 Example 8-3b

Determine whether and are inverse functions. Answer: The functions are inverses since both compositions equal x. 11/29/2018 Example 8-3c

Homework - Honors See Syllabus 7.8 pp. 393-394: 18, 20-36 even, 38-44 11/29/2018

Homework See Syllabus 7.8 PP 393-394 14-36 even, 38-43. 11/29/2018