Inverse & Direct Variation Simplifying Expressions

Slides:

Advertisements

Similar presentations

Jeopardy Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300 Q $400 Q $500 Final Jeopardy.

Advertisements

Lesson 8-1: Multiplying and Dividing Rational Expressions

Unit 1 – Foundation for Algebra (Part 1) Jeopardy Review.

The Discriminant Check for Understanding – Given a quadratic equation use the discriminant to determine the nature of the roots.

Jeopardy Solving Equations With Pictures Solving Equations With two Variables The Distributive Property Final Jeopardy Evaluating the Expression So you.

EXAMPLE 5 Write a joint variation equation The variable z varies jointly with x and y. Also, z = –75 when x = 3 and y = –5. Write an equation that relates.

9.1 Multiplying and Dividing Rational Expressions

12.1 – Simplifying Rational Expressions A rational expression is a quotient of polynomials. For any value or values of the variable that make the denominator.

Chapter 11.1 Common Core – A.APR.7 …add, subtract, multiply, and divide rational expressions. Objective – To simplify rational expressions.

Station A: Linear Functions: Solve each equation Solve for the specified variable: Write an equation in slope-intercept form for the line.

Section 6.1 Rational Expressions. OBJECTIVES A Find the numbers that make a rational expression undefined.

9.3 Graphing Rational Functions Algebra II w/ trig.

Simplifying Rational Expressions where P(x) and Q(x) are polynomials, Q(x) ≠ 0. Just as we simplify rational numbers (fractions) in arithmetic, we want.

Rational Expressions Section 0.5. Rational Expressions and domain restrictions Rational number- ratio of two integers with the denominator not equal to.

Unit 7—Rational Functions Rational Expressions Quotient of 2 polynomials.

Rational Expressions.

R7 Rational Expressions. Rational Expressions An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero.

9.1 Multiplying and Dividing Rational Expressions Alg 2.

 Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero.

Do Now: Solve for x in the following equation: Hint: and.

Solving Polynomial Equations – Factoring Method A special property is needed to solve polynomial equations by the method of factoring. If a ∙ b = 0 then.

DIRECT VARIATION In a DIRECT VARIATION, as one quantity increases, the other quantity increases. Equation of Direct Variation.

A Quadratic Equation is an equation that can be written in the form Solving Quadratic Equations – Factoring Method Solving quadratic equations by the factoring.

Warm-up p 499 check skills (1 – 12). Quiz 1.If z=30 when x=3 and y=2, write the function that models the relationship “z varies directly with x and inversely.

10-1 Inverse Variation 10-2 Rational Functions 10-3 Simplifying Rational Expressions 10-4 Multiplying and Dividing Rational Expressions 10-5 Adding and.

 Direct Variation Function – A function that can be modeled with the equation y = kx.

Jeopardy $100 Synthetic Division SD : Remainder Theorem FactoringVOID $200 $300 $400 $500 $400 $300 $200 $100 $500 $400 $300 $200 $100 $500 $400 $300.

An equation in the form … … can be solved using two methods discussed previously. Solving Equations Containing Trinomials 1.Factoring Method 2.Graphing.

Multiplying and Dividing Rational Expressions

Review Know all of the formulas of variations.

2.4 Writing Equations of Lines. We’ve learned to graph given an equation. Now we’ll learn to write the equation given the graph There are three ways.

2.4 Writing Equations of Lines p. 91. Learning Target I can write equations of a line.

Chapter 7: Rational Algebraic Functions Section 7-11: Variation Functions.

Rational Functions. Do Now Factor the following polynomial completely: 1) x 2 – 11x – 26 2) 2x 3 – 4x 2 + 2x 3) 2y 5 – 18y 3.

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

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:

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

Table of Contents Solving Polynomial Equations – Factoring Method A special property is needed to solve polynomial equations by the method of factoring.

Please complete the Prerequisite Skills on Page 548 #4-12

Jeopardy Factoring Functions Laws of Exponents Polynomial Equations Q $100 Q $200 Q $300 Q $400 Q $100 Q $200 Q $300 Q $400 Final Jeopardy Q $500.

X = Y. Direct variation X 1 X = Y 1 Y 2.

Joint and Combined Variation Review of Variations Direct Variation Inverse Variation Formula General Equation.

Math 20-1 Chapter 6 Rational Expressions and Equations 6.1 Rational Expressions Teacher Notes.

11.3 Solving Radical Equations Definitions & Rules Simplifying Radicals Practice Problems.

CHAPTER 9 SECTION 3 RATIONAL FUNCTIONS AND GRAPHS Algebra 2 Notes May 21, 2009.

9.4 Rational Expressions (Day 1). A rational expression is in _______ form when its numerator and denominator are polynomials that have no common factors.

Math 20-1 Chapter 6 Rational Expressions and Equations 7.1 Rational Expressions Teacher Notes.

Ratio and Proportions Percents Direct and Inverse Variation.

Direct Variation Equations

Adv. Alg., Chapter 9 Algebra 2 – Chapter 7 JEOPARDYJEOPARDY.

Rational Functions…… and their Graphs

Equation of Direct Variation

Definition of a Polynomial Inequality

Chapter 5 Polynomials Describe Graphs Synthetic Division

The Discriminant Check for Understanding –

Solve a system of linear equation in two variables

Welcome to Jeopardy! Rational Expressions.

Graphing Simple Rational Functions p 381

Algebra Section 11-1 : Rational Expressions and Functions

Appendix A.4 Rational Expression.

The Discriminant Check for Understanding –

Jeopardy Rational Exponents. Laws of Exponents Polynomials Q $100

Rational Functions A rational function f(x) is a function that can be written as where p(x) and q(x) are polynomial functions and q(x) 0 . A rational.

Expressions & Equations Jeopardy

Section 2.9: Solving Inequalities in One Variable

Solving Equations Containing Trinomials

Bell Work Combine all the like terms

Presentation transcript:

Inverse & Direct Variation Simplifying Expressions Jeopardy! Final Jeopardy Inverse & Direct Variation Rational Equations Identifying Graphs Simplifying Expressions Graphing Functions 100 200 300 400 500

Inverse & Direct Variation 100 Does the following chart represent direct or inverse variation? Time Distance 1 hr 5 mi 3 hrs 15 mi 5 hrs 25 mi 10 hrs 50 mi Category 1 - 10 Answer

Inverse & Direct Variation 200 x and y vary inversely. Use the given values to write an equation relating x and y. Category 1 - 20 Answer

Inverse & Direct Variation 300 l varies jointly with m and n. Use the given values to write an equation relating l, m, and n. Answer

Inverse & Direct Variation 400 z is related directly with x and inversely with y. Use the given values to write an equation relating x, y, and z. Answer

Inverse & Direct Variation 500 Give an example (that we have not discussed in class) of a situation that has variables which are inversely related. Answer

Rational Equations 100 Answer

Rational Equations 200 Answer

Rational Equations 300 Answer

Rational Equations 400 Answer

Rational Equations 500 Answer

Identifying Graphs 100 Which graph does the following equation represent? Answer

Identifying Graphs 200 Which graph does the following equation represent? Answer

Identifying Graphs 300 Which graph does the following equation represent? Answer

Identifying Graphs 400 Which equation does the following graph represent? Answer

Identifying Graphs 500 Which graph does the following equation represent? Answer

Simplifying Expressions 100 Answer

Simplifying Expressions 200 Answer

Simplifying Expressions 300 Answer

Simplifying Expressions 400 Answer

Simplifying Expressions 500 Answer

Graph the following function. Put your answer on the board. Graphing Functions 100 Graph the following function. Put your answer on the board. Answer

Graph the following function. Put your answer on the board. Graphing Functions 200 Graph the following function. Put your answer on the board. Answer

Graph the following function. Put your answer on the board. Graphing Functions 300 Graph the following function. Put your answer on the board. Answer

Graph the following function. Put your answer on the board. Graphing Functions 400 Graph the following function. Put your answer on the board. Answer

Graph the following function. Put your answer on the board. Graphing Functions 500 Graph the following function. Put your answer on the board. Answer

Inverse & Direct Variation Answer: Inverse & Direct Variation 100 Direct

Inverse & Direct Variation Answer: Inverse & Direct Variation 200

Inverse & Direct Variation Answer: Inverse & Direct Variation 300

Inverse & Direct Variation Answer: Inverse & Direct Variation 400

Inverse & Direct Variation Answer: Inverse & Direct Variation 500 I decide!

Answer: Rational Equations 100

Answer: Rational Equations 200

Answer: Rational Equations 300

Answer: Rational Equations 400

Answer: Rational Equations 500

Answer: Identifying Graphs 100

Answer: Identifying Graphs 200

Answer: Identifying Graphs 300

Answer: Identifying Graphs 400

Answer: Identifying Graphs 500

Simplifying Rational Expressions Answer: Simplifying Rational Expressions 100

Simplifying Rational Expressions Answer: Simplifying Rational Expressions 200

Simplifying Rational Expressions Answer: Simplifying Rational Expressions 300

Simplifying Rational Expressions Answer: Simplifying Rational Expressions 400

Simplifying Rational Expressions Answer: Simplifying Rational Expressions 500

Graphing Rational Functions Answer: Graphing Rational Functions 100

Graphing Rational Functions Answer: Graphing Rational Functions 200

Graphing Rational Functions Answer: Graphing Rational Functions 300

Graphing Rational Functions Answer: Graphing Rational Functions 400

Graphing Rational Functions Answer: Graphing Rational Functions 500

Final Jeopardy

Give the definition of a rational function.

A rational function has the form: where p(x) and q(x) are polynomials and q(x) does not equal zero.