Algebra 2 Notes April 23, 2009. 1) 2.) 4.) 5.) 13.) domain: all real #s 14.) domain: all real #s 16.) domain: all real #s 17.) domain: all real #s 22.)

Slides:



Advertisements
Similar presentations
Function f Function f-1 Ch. 9.4 Inverse Functions
Advertisements

Linear Relations and Functions
Concepts 1 and 2. A (, ) B (, ) C (, ) D (, ) E (, )
2.1 Relations and Functions. In this chapter, you will learn: What a function is. Review domain and range. Linear equations. Slope. Slope intercept form.
Warm Up Solve for y. 1. x = 3y –7 2. x = 3. x = 4 – y 4. x = y2 y + 5
RELATIONS AND FUNCTIONS
Warm Up 1. 5x – 2 when x = – t 2 when 3. when x = Give the domain and range for this relation: {(1, 1), (–1, 1), (2, 4), (–2, 4),
1.2 Represent Functions as Rules and Tables
Algebra II w/ trig.  Coordinate Plane  Ordered pair: (x, y)  Relation: a set of ordered pairs(mapping, ordered pairs, table, or graphing)  Domain:
4-1: Relations and Functions
Warm-Up Graph the point (2, -3) If
Notes 4.6– FORMALIZING RELATIONS AND FUNCTIONS
Objectives & Vocabulary
4-3 Relations Objective: Students will represent relations as sets of ordered pairs, tables, mappings, and graphs. Students will find the inverse of a.
Objectives Determine whether the inverse of a function is a function.
Lesson 4-4 Example Determine the slope of the function y = 5x – 2. Step 1Complete a function table for the equation.
Holt Algebra Identifying Linear Functions Give the domain and range of each relation. –4 – x y x y
Functions Algebra. Functions Definitions Relation – a set of coordinate points (x, y) Domain – the x-values, input Range – the y-values, output Function.
Warm Up. FUNCTIONS DEFINED Essential Question: How can you determine if a relation is a function?
Functions: Definitions and Notation 1.3 – 1.4 P (text) Pages (pdf)
What is the domain of the following relation? (use correct notation) { (1, 3), (4, 5.5), (6, 9), (10, 0) }
Chapter 2 Section 3. Introduction to Functions Goal:Find domain and range, determine if it’s a function, use function notation and evaluate. Definition.
Holt Algebra Identifying Linear Functions Warm Up 1. Solve 2x – 3y = 12 for y. 2. Graph for D: {–10, –5, 0, 5, 10}.
Holt McDougal Algebra Properties of Quadratic Functions in Standard Form This shows that parabolas are symmetric curves. The axis of symmetry is.
DOMAIN AND RANGE Section Functions Identify relations, domains, and ranges.
Ch Relations and Functions Objective: To be able to determine whether a given relation is a function.
Lesson 6-6 Example Example 2 Graph y = 3x + 2 and determine the slope of the line. 1.Complete a function table for the equation.
Graphing Test Review Algebra. Express the relation as a set of ordered pairs and the inverse. xy
7.5 – Graphing Square Roots and Cube Roots
Relations and Functions. Def: Relation A relation is a set of ordered pairs. The domain is the set of all abscisses (x-values) and the range is the set.
Georgia Performance Standard (GPS): MM4A1 “Students Will Explore Rational Functions.”
Relations and Functions By: Jeffrey Bivin Lake Zurich High School Last Updated: November 14, 2007.
CHAPTER 6 SECTION 6 : FUNCTIONS AND THEIR INVERSES.
MATH II – Math I review
Relations and Functions Intermediate Algebra II Section 2.1.
Domain and Range of a Graph. Domain The domain of a graph is displayed by the set of all possible x-values or abscissas. In this example, the domain continues.
2.1 GRAPHING LINEAR EQUATIONS GOAL: FIND DOMAIN AND RANGE. DETERMINE IF RELATIONS ARE FUNCTIONS. GRAPH LINEAR EQUATIONS.
12.1 functions Copy planner. functions Functions are basically the same as equations, they are just written differently. F(x) means the function of “x”
Inverses of Relations and Functions
4 Inverse, Exponential, and Logarithmic Functions © 2008 Pearson Addison-Wesley. All rights reserved.
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.
Unit 1: Functions Review Determining if a relation is a function or not a function (NOT a function if it fails the vertical line test; NOT a function if.
Holt McDougal Algebra Logarithmic Functions Write equivalent forms for exponential and logarithmic functions. Write, evaluate, and graph logarithmic.
Objective: Students will identify the domain and range of ordered pairs and graphs.
UNIT 3 VOCABULARY UNIT 3 VOCABULARY THIS UNIT CONTAINS A LARGE AMOUNT OF NEW, VERY MATH SPECIFIC VOCABULARY TODAY, WE ARE GOING TO START A REFERENCE.
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.
Chapter 2 Section 1 Relations and Functions Algebra 2 Notes January 8, 2009.
Ch. 9.1 Inverse Variation.
Holt Algebra Inverses of Relations and Functions Graph and recognize inverses of relations and functions. Find inverses of functions. Objectives.
Section 4.2.  Label the quadrants on the graphic organizer  Identify the x-coordinate in the point (-5, -7)
Ch 9 – Properties and Attributes of Functions 9.5 – Functions and their Inverses.
Holt McDougal Algebra 1 Relations and Functions GSE Algebra 1 Unit 2B D1 Identifying Functions Essential Questions How can I identify functions from various.
Algebra 2 Foundations, pg 64  Students will be able to graph relations and identify functions. Focus Question What are relations and when is a relation.
Holt Algebra Relations and Functions Warm Up 1. Express the relation {(1,5), (2, 3), (3,2), (4,1)} as a table, as a graph, and as a mapping diagram.
7.4 Inverse Trig Functions. For a function to have an inverse it must be one-to- one. One-to-one functions have to pass the horizontal line test. Each.
SECTION 1.2 Functions. Relations A relation is a set of ordered pairs.  Set of x-values is the DOMAIN  Set of y-values is the RANGE If each x-value.
2.2 Graphs of Equations.
6-7 Inverse Relations and Functions
Inverse Functions 5.3 Chapter 5 Functions 5.3.1
Ch 1.6: Inverse of Functions and Relations
One-to-one and Inverse Functions
Notes Over 7.4 Finding an Inverse Relation
One-to-One Functions;
One-to-one and Inverse Functions
Section 3.1 Functions.
2.1 Functions.
Name the quadrant or the axis on which the following points lie.
Equations & Graphing Algebra 1, Unit 3, Lesson 5.
Presentation transcript:

Algebra 2 Notes April 23, 2009

1) 2.) 4.) 5.) 13.) domain: all real #s 14.) domain: all real #s 16.) domain: all real #s 17.) domain: all real #s 22.) 8 23.) ) 20 31) 1 32) 25 33) -3 40)

 Relations pair an element of its domain with an element of its range  The inverse pairs an element of the range with an element of the domain:  Example: (x, y) is the ordered pair of a relation (y, x) is the ordered pair of the inverse

 Find the inverse of the following equations: ◦ Is the inverse a function?

 Consider the following function: ◦ Find the domain (x-values) and range (y-values) of ◦ Find (inverse of ) ◦ Is the inverse a function?

 Consider the following function: ◦ Find the domain (x-values) and range (y-values) of ◦ Find (inverse of ) ◦ Is the inverse a function?

 Consider the following equation: ◦ Find the inverse ( ) of the function ◦ Find ◦ What conclusion can you make??

 Page 410 #1, 5, 6, 9, 11, 12, 23, 24, 29, 30, 31-34, 44