Functions and Relations 2 Page 3 We are going to work on some of the exercises today:

Slides:

Advertisements

Similar presentations

Section 3.4 Objectives: Find function values

Advertisements

Warm up 1. Solve 2. Solve 3. Decompose to partial fractions -1/2, 1

Describing the graph of a Parabola

Copyright © 2013, 2009, 2005 Pearson Education, Inc.

LIAL HORNSBY SCHNEIDER

Rational Expressions Simplifying. Simplifying Rational Expressions The objective is to be able to simplify a rational expression.

1.3 Functions Domain and Range Function notation Piecewise functions

Square-Root Functions

1.7, page 209 Combinations of Functions; Composite Functions Objectives Find the domain of a function. Combine functions using algebra. Form composite.

Domain and Range Lesson 2.2. Home on the Range What kind of "range" are we talking about? What does it have to do with "domain?" Are domain and range.

12.2 Functions and Graphs F(X) = x+4 where the domain is {-2,-1,0,1,2,3}

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

Honors Topics.  You learned how to factor the difference of two perfect squares:  Example:  But what if the quadratic is ? You learned that it was.

FUNCTIONS : Domain values When combining functions using the composite rules, it is necessary to check the domain for values that could be restricted.

7.5 Graphs Radical Functions

Section 9.1: Evaluating Radical Expressions and Graphing Square Root and Cube Root Functions.

11-1 Square-Root Functions Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview.

Definition of a Function A function is a set of ordered pairs in which no two ordered pairs of the form (x, y) have the same x-value with different y-values.

Sec. 1.3 – 1.4 Functions and Their Graphs

Each element in A must be matched with an element in B Ex– (0,3) (3,2) (9,4) (12,5) Some elements in the range may not be matched with the domain. Two.

3.1 Functions and their Graphs

Functions: Definitions and Notation 1.3 – 1.4 P (text) Pages (pdf)

 Form of notation for writing repeated multiplication using exponents.

Logarithmic Functions & Graphs, Lesson 3.2, page 388 Objective: To graph logarithmic functions, to convert between exponential and logarithmic equations,

§ 2.3 The Algebra of Functions – Finding the Domain.

Chapter 3: Functions and Graphs 3.1: Functions Essential Question: How are functions different from relations that are not functions?

Other Types of Equations Solving an Equation by Factoring The Power Principle Solve a Radical Equation Solve Equations with Fractional Exponents Solve.

Chapter 1 Functions and Graphs Copyright © 2014, 2010, 2007 Pearson Education, Inc Combinations of Functions; Composite Functions.

Introduction As is true with linear and exponential functions, we can perform operations on quadratic functions. Such operations include addition, subtraction,

Dear Power point User, This power point will be best viewed as a slideshow. At the top of the page click on slideshow, then click from the beginning.

Graph Square Root and Cube Root Functions

Interpretation of Domain and Range of a function f.

Chapter 7 Day 3 Book Section 7.5 Get 2 grids for the 2 shift problems!

10-3C Graphs of Radical Equations If you do not have a calculator, please get one from the back wall! The Chapter 10 test is a NON calculator test! Algebra.

Fractional Equations and Extraneous Solutions

Table of Contents Rational Expressions and Functions where P(x) and Q(x) are polynomials, Q(x) ≠ 0. Example 1: The following are examples of rational expressions:

Radical Expressions and Functions Find the n th root of a number. 2.Approximate roots using a calculator. 3.Simplify radical expressions. 4.Evaluate.

Standard 44: Domains of Rational Expressions BY: ABBIE, ABBY, HARLEY, COLE.

Bell Quiz. Objectives Simplify rational expressions. Find undefined or excluded values for rational expressions.

Chapter 2 Functions and Graphs Copyright © 2014, 2010, 2007 Pearson Education, Inc Combinations of Functions; Composite Functions.

Aim: How do we solve rational inequalities? Do Now: 2. Find the value of x for which the fraction is undefined 3. Solve for x: HW: p.73 # 4,6,8,10,14.

Lesson 2.7, page 346 Polynomial and Rational Inequalities.

6.6 Function Operations Honors. Operations on Functions Addition: h(x) = f(x) + g(x) Subtraction: h(x) = f(x) – g(x) Multiplication: h(x) = f(x) g(x)

Section 7.6 Functions Math in Our World. Learning Objectives  Identify functions.  Write functions in function notation.  Evaluate functions.  Find.

Section 1 Chapter Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives 2 Additional Graphs of Functions 11.1 Recognize the graphs of.

Properties of Elementary Functions

Rational Functions and Their Graphs Objective: Identify and evaluate rational functions and graph them.

Algebra 1 Section 9.2 Simplify radical expressions

Domain & Range 3.3 (From a graph & equation).

Properties of Functions

DOMAINS OF FUNCTIONS Chapter 1 material.

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

Domain and Range Lesson 2.2.

Solving Equations Containing

7.5 Graphs Radical Functions

Solving Equations Containing

Solving Equations Containing

Functions Definition: A function from a set D to a set R is a rule that assigns to every element in D a unique element in R. Familiar Definition: For every.

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

Appendix A.4 Rational Expression.

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

Warm Up Find each square root Solve each inequality.

Notes Over 8.3 Simplifying Natural Base Expressions

1.6 - Relations.

Section 8.4 – Graphing Rational Functions

Solving Equations Containing

Presentation transcript:

Functions and Relations 2 Page 3 We are going to work on some of the exercises today:

Page 3 For a question like this, they give you a domain. This is called a restricted, or limited, domain. These are the only numbers you are allowed to use to find the range. So lets get a table built using y=.

This means that the domain may have values that make the expression undefined! This expression is a fraction. Therefore, there may be values that make it undefined. We need to check: Since 6 makes the denominator undefined, then choice 3 would have a restricted domain. The rest of the choices have no restrictions. That means that you could sub any value in for x and it will map to a y value! Notation:OR: Page 3

This time, we can not have a negative under the radical, so we need to check for it! Page 3

Since they give us the domain, we can sub in the domain values for x and determine the range values (y). Page 3

Page 4

Think: is there any number, when squared, that isn’t greater than or equal to -1? Therefore the domain is the set of all real numbers! Page 4 Since we have a fraction, we have to find the values of x that make the denominator undefined. Since the denominator is a radical, the values of x must also be greater than or equal to 0.

To do this, we can use the graphing calculator! Page 4