Section 8-1: Introduction to Irrational Algebraic Functions.

Slides:

Advertisements

Similar presentations

THE ABSOLUTE VALUE FUNCTION. Properties of The Absolute Value Function Vertex (2, 0) f (x)=|x -2| +0 vertex (x,y) = (-(-2), 0) Maximum or Minimum? a =

Advertisements

7.8 Equations Involving Radicals. Solving Equations Involving Radicals :  1. the term with a variable in the radicand on one side of the sign.  2. Raise.

To Solve Equations which Involve Exponents.

7.3 Solving Radical Equations

Section 3.2 Beginning on page 104

Other Types of Equations

TODAY IN ALGEBRA…  Learning Goal: 7.2 You will solve systems of linear equations by Substitution  Independent Practice.

Section 6.4 Exponential and Logarithmic Equations

Chapter 8: Irrational Algebraic Functions

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

Solving equations Section 1.4.

 Factoring (3)  Solving Quadratics (3)  Imaginary Numbers (2)  Extraneous Solutions (1) Functions:  Finding Zeroes (2)  Finding Minimum via TI 84+

SECTION 7-3: SOLVING RADICAL EQUATIONS Solve equations that contain radicals or rational exponents.

Unit 6 GA2 Test Review. Find the indicated real n th root ( s ) of a. a. n = 3, a = –216 b. n = 4, a = 81 SOLUTION b. Because n = 4 is even and a = 81.

1. Write 15x2 + 6x = 14x2 – 12 in standard form.

Do Now: Find all real zeros of the function.

SOLVING SYSTEMS ALGEBRAICALLY SECTION 3-2. SOLVING BY SUBSTITUTION 1) 3x + 4y = 12 STEP 1 : SOLVE ONE EQUATION FOR ONE OF THE VARIABLES 2) 2x + y = 10.

Final Exam Review Pages 1-4  System of Equations  Exponent Rules  Simplifying radicals.

Functions Section 1.4. Relation The value of one variable is related to the value of a second variable A correspondence between two sets If x and y are.

The Fundamental Theorem of Algebra 1. What is the Fundamental Theorem of Algebra? 2. Where do we use the Fundamental Theorem of Algebra?

WRITE LINEAR EQUATIONS IN SLOPE- INTERCEPT FORM December 2, 2013 Pages

Linear Systems of Equations Section 3.1. What is a “system” of equations?

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

Given a quadratic equation use the discriminant to determine the nature of the roots.

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

By the end of this section, you will be able to: 1. Determine the number and type of roots for a polynomial equation; 2. Find the zeros of a polynomial.

Notes Over 7.6 Solving a Simple Radical Equation Solve the equation. Check your solution.

Radical expressions, rational exponents and radical equations ALGEBRA.

7.5 Roots and Zeros Objectives:

Radical Equation Equation with a variable under radical sign Extraneous Solutions: Extra solutions that do not satisfy original equation because of the.

TODAY IN ALGEBRA 2.0…  Review: Solving Linear Systems by Graphing  Learning Goal 1: 3.2 Solving Linear Systems by Substitution with one equation solved.

Solving Exponential and Logarithmic Equations Section 3.4.

Solving Radical Equations and Inequalities Section 5.8.

Do Now Determine which numbers in the set are natural, whole, integers, rational and irrational -9, -7/2, 5, 2/3, √2, 0, 1, -4, 2, -11 Evaluate |x + 2|,

Algebra 1 Section 2.1 Graph and order real numbers Find absolute values and opposites The numbers used in algebra 1 are real numbers. They include whole.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 12.6 Systems of Nonlinear Equations.

Chapter 8 Quadratic Functions.

Systems of Nonlinear Equations

Equations Quadratic in form factorable equations

Systems of Nonlinear Equations

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.

Sullivan Algebra and Trigonometry: Section 6.3 Exponential Functions

College Algebra Chapter 2 Functions and Graphs

Notes Over 4.7 Solving an Equation Graphically

Systems of Nonlinear Equations

Appendix A.5 Solving Equations.

Solve Quadratic Systems

SECTION 9-3 : SOLVING QUADRATIC EQUATIONS

College Algebra Chapter 3 Polynomial and Rational Functions

Graphing Linear Equations

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.

Chapter 3 Section 6.

Using Factoring To Solve

College Algebra Chapter 2 Functions and Graphs

Factoring Using Special Patterns General Algebra II

Chapter 3 Graphs and Functions.

Chapter 3 Section 6.

SECTION 10-4 : RADICAL EQUATIONS

Solving a Radical Equation

Algebra 1 Section 6.3.

Solving Linear Equations by Graphing

Sullivan Algebra and Trigonometry: Section 6.2

Equations Quadratic in form factorable equations

Name ________________________________________________

Exponential Functions

Section 2.9: Solving Inequalities in One Variable

College Algebra 1.6 Other Equations

Example 1: Solving Rational Equations

Presentation transcript:

Section 8-1: Introduction to Irrational Algebraic Functions

Learn things about an irrational algebraic function by pointwise plotting of its graph and other algebraic techniques.

An irrational algebraic function is a function in which the independent variable appears under a radical sign or in a power with a rational number for its exponent. Example:

Section 8-2: Graphs of Irrational Functions

Given the equation of an irrational algebraic function, find f(x) when x is given and find x when f(x) is given and plot the graph.

Two interesting things happen when we evaluate the function: If you choose a value of x where x < -2, f(x) will be imaginary and thus not show up on the graph. Secondly, if you substitute a number such as f(x) = 1, and try to solve for x, we run into a problem. Let’s look what will happen.

When solving the equation, we will get: Is this possible? Why or why not? The number 2 is what we call an extraneous solution.

What is the least value of x for which there is a real number value of f(x)? Plot the graph of function f using a suitable domain. What does the f(x) intercept equal? What does the x intercept equal? Find two values of x for which f(x) = -5. Find one value of x for which f(x) = -3. Show that there are no values of x for which f(x) = -8. f(x) reaches a minimum value somewhere between x = -4 and x = 0. Approximately what is the value of x? Approximately what is the minimum value?

Page 416: #5 (finish if necessary)