Radical Functions Standard 5a: Use sign patterns to determine the domain of a rational function.

Slides:

Advertisements

Similar presentations

Unit 4Radicals Complex numbers.

Advertisements

We will find limits algebraically

It’s a Dog’s World! Multiplying and Dividing Square Roots.

Examples for Rationalizing the Denominator Examples It is improper for a fraction to have a radical in its denominator. To remove the radical we “rationalize.

9.3 Simplifying Radicals.

Functions Basic Concepts Value (Image), Domain, Range, Graph.

SQUARE ROOT METHOD. Simplify Radicals A. Single Ex.

Day 5 Simplify each expression: Solving Quadratic Equations I can solve quadratic equations by graphing. I can solve quadratic equations by using.

Solving Quadratic Equaitons Section 3.1 beginning on page 94.

Learning Objectives for Section 2.1 Functions

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

Solving Quadratic Equations by the Quadratic Formula

Simplify Rational Expressions

Square roots of numbers are called numbers. Unit Imaginary Number i is a number whose square is -1. That is, In other words,. negative imaginary.

5.3 Solving Quadratic Equations by Finding Square Roots Goals: 1. Solve quadratic equations by finding square roots 2. using quadratic models in real.

Lesson 2-7 Square Roots and Real Numbers. Definitions: Square Root- one of two equal factors of a number. Perfect Square- A number, like 64, whose square.

Jim Smith JCHS. Perfect Squares If You Multiply A Number By It’s Self, You Get A Perfect Square 1x1 = 1 2x2 = 4 3x3 = 9 1, 4, 9, 16, 25, 36, 49, 64, 81,

Unit 1 Review Standards 1-8. Standard 1: Describe subsets of real numbers.

The Quadratic Formula Students will be able to solve quadratic equations by using the quadratic formula.

10-4 Solving Quadratic Equations by Using the Quadratic Formula

Rational Functions and Domains where P(x) and Q(x) are polynomials, Q(x) ≠ 0. A rational expression is given by.

Solving Quadratic Equaitons Section 3.1 beginning on page 94.

Chapter 4: Polynomial and Rational Functions. 4-2 Quadratic Equations For a quadratic equation in the form ax 2 + bx + c = 0 The quadratic Formula is.

9.2 THE DISCRIMINANT. The number (not including the radical sign) in the quadratic formula is called the, D, of the corresponding quadratic equation,.

Square Root Function Graphs Do You remember the parent function? D: [0, ∞) R: [0, ∞) What causes the square root graph to transform? a > 1 stretches vertically,

Radicals (Square Roots). = 11 = 4 = 5 = 10 = 12 = 6 = 7 = 8 = 9 = 2.

Absolute Value Absolute Value is the distance a number is away from zero on the number line. Find.| 4 | 4 | – 4 | 4 * Absolute Value Is ALWAYS POSITIVE!!!!*

Principle of Square Roots. For any nonnegative real number k, if x 2 = k, then x = or x =. -

Rationalizing the denominator. Rational numbers Another word for ‘fraction’ is ratio. Any number that can be written as a fraction is a rational number.

Rational Inequalities Standard 4f: Use sign patterns to solve rational inequalities.

5-5 ROOTS OF REAL NUMBERS Objective: Students will be able to simplify radicals.

5.2 Solving Quadratic Equations by Factoring 5.3 Solving Quadratic Equations by Finding Square Roots.

Ticket in the Door 3-29 Solving Radical Inequalities Solve the following inequalities for x. Show work!

Rational Function Extreme Points Standard 4e: Find the extreme points of a rational function (remember that extreme points are y values)

Traits & Graphs of Radical Functions Standard 8c: Find the critical values and extreme points of radical functions Standard 8d: Find all the traits and.

Natural Numbers Where do the natural numbers start? 1 Write them in set notation {1, 2, 3,... }

Warm Up Simplify each expression

6.5 The Quadratic Formula and the Discriminant

Functions Domain and Range.

Section 2.6 Rational Functions Part 2

Rational Functions.

Today in Pre-Calculus Turn in info sheets

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

Do Now: Can you input all real numbers into the x variable in the following functions? If not what numbers can x not take on?

3.4 Notes Irrational Numbers.

3.7 Extension Activity.

5.3 Solving Quadratic Equations by Finding Square Roots

Questions over HW?.

4.5 Solving Quadratic Equations by Finding Square Roots

Radical Function Review

1. Use the quadratic formula to find all real zeros of the second-degree polynomial

Objectives Rewrite radical expressions by using rational exponents.

Rational Functions and Asymptotes

Objectives Identify linear functions and linear equations.

Parent Functions.

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.

Parent Functions.

Appendix A.4 Rational Expression.

3.5 Polynomial and Rational Inequalities

Questions over HW?. Skills Check Radical Operations and Solving by Square Roots after HW Check.

Imaginary Numbers though they have real world applications!

Warm Up Simplify 1)

Day 5  Happy Friday!!.

Objective: To graph square root functions

Unit 1.3 Part A Learning Goal:

5. Continuity on an Interval

Dividing Radical Expressions

Domain & Range Unit 8.

Square Root Functions and Geometry

Presentation transcript:

Radical Functions Standard 5a: Use sign patterns to determine the domain of a rational function

Find the domain of What values of x give us something with a real number square root? Now make a sign pattern number line + − + −

Find the domain of What does this tell us about how the graph will look? Note the intervals of x for which this graph exists.

Find the domain of What values of x give us something with a real number square root? We already know from the previous example that when But we also have to account for values of x for which Remember that we can’t include x = 1 because the denominator can’t be zero

Find the domain of What values of x give us something with a real number square root? when when DNE – + – + −

Find the domain of