The Modulus Function Objectives: Understand what an absolute value is. Solve equations and inequalities involving modulus. Graph modulus functions.

Slides:

Advertisements

Similar presentations

1.4 – Shifting, Reflecting, and Stretching Graphs

Advertisements

Polynomial Inequalities in One Variable

Warm-Up Explain how you made each match (Without a calculator!)

3-3 Solving Systems of Inequalities by Graphing

1 of 7 Pre-Calculus2 Chapter 10 Section 8 Warm up Write the equation in standard form of Write the equation in standard form of Then find the coordinates.

The modulus function The modulus of x, written  x  and is defined by  x  = x if x  0  x  = -x if x < 0. Sketch of y =  x  y x y =  x  y = x.

Systems of Linear Inequalities.  Two or more linear inequalities together form a system of linear inequalities.

Solving quadratic equations Factorisation Type 1: No constant term Solve x 2 – 6x = 0 x (x – 6) = 0 x = 0 or x – 6 = 0 Solutions: x = 0 or x = 6 Graph.

1.8 Solving Absolute Value Equations and Inequalities

N 58 Graphical Solutions to Quadratic Functions Subject Content Reference: N6.7h GCSE Maths Number & Algebra.

Slide Systems of Linear Equations A system of linear equations consists two or more linear equations.

Topics: Topic 1: Solving Linear Equations Topic 2: Solving Quadratic Equations Topic 3: Solving Proportions involving linear and quadratic functions. Topic.

Linear Inequalities Foundation Part I. An INEQUALITY shows a relationship between two variables, usually x & y Examples –y > 2x + 1 –y < x – 3 –3x 2 +

Sketching quadratic functions To sketch a quadratic function we need to identify where possible: The y intercept (0, c) The roots by solving ax 2 + bx.

Solving equations Section 1.4.

Quadratic Inequalities Lesson Definition Recall the quadratic equation ax 2 + bx + c = 0 Replace = sign with, ≤, or ≥ makes it a quadratic inequality.

CA STANDARDS 20.0: Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations. Agenda 1.) Lesson.

Chapter 1 : Functions Sept 29, Solving Quadratic Inequalities Graphically 1.Write in standard form F(x) > 0. 2.Factor if possible. Find zeros of.

3.6 Solving Absolute Value Equations and Inequalities

Chapter 2: Equations and Inequalities

Review #1. SOLVING LINEAR EQUATIONS, INEQUALITIES AND ABSOLUTE VALUES  Multi-Step Equations  Solve each equation. Check your solution.  1) 4x – 12.

2.1 – Quadratic Functions.

Solving Linear Inequalities Lesson 5.5 linear inequality: _________________________________ ________________________________________________ solution of.

“Teach A Level Maths” Vol. 1: AS Core Modules

Solving Open Sentences Involving Absolute Value

Absolute Value Equations & Inequalities. Review: Absolute Value The magnitude of a real number without regard to its sign. OR Distance of value from zero.

Section 4.3 Solving Absolute Value Equations and Inequalities

MTH 065 Elementary Algebra II Chapter 6 – Polynomial Factorizations and Equations Section 6.1 – Introduction to Polynomial Factorizations and Equations.

5-5 Solving Quadratic Equations Objectives:  Solve quadratic equations.

1.8 Solving Absolute Value Equations and Inequalities Objectives: Write, solve, and graph absolute value equations and inequalities in mathematical and.

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

Topics: Topic 1: Solving Linear Equations Topic 2: Solving Quadratic Equations Topic 3: Solving Proportions involving linear and quadratic functions. Topic.

Chapter 4: Systems of Equations and Inequalities Section 4.3: Solving Linear Systems Using Graphs.

Chapter 4: Systems of Equations and Inequalities Section 4.7: Solving Linear Systems of Inequalities.

CHAPTER 10 LESSON OBJECTIVES. Objectives 10.1 Students will be able to: Identify quadratic functions and determine whether they have a minimum or maximum.

Warm Up: Graph the following inequality. Test Point: (0,0) Section 9.4 – Systems of Inequalities Graphing Calculator Required (3/2)x+2.

Solving Systems of Equations Graphing Linear Inequalities.

Solving Systems of Linear and Quadratic Equations.

Algebra 1 Section 7.6 Solve systems of linear inequalities The solution to a system of linear inequalities in two variable is a set of ordered pairs making.

10.3 Solving Quadratic Equations – Solving Quadratic Eq. Goals / “I can…”  Solve quadratic equations by graphing  Solve quadratic equations using.

Warm-Up: Solve and Graph  1.  2.. CHAPTER 6 SECTION 4 Solving Absolute-Value Equations and Inequalities.

5.4 – Completing the Square

Chapter 3 – Algebra III 03 Learning Outcomes

Objectives: Graph (and write) inequalities on a number line.

Solving and Graphing Absolute Value Inequalities

3.3 – Solving Systems of Inequalities by Graphing

Quadratic Inequalities with 1 Variable (Interval analysis)

Section 7.5 Systems of Linear Inequalities

Solving Nonlinear Systems

Solving Quadratic Equations by the Complete the Square Method

Graphing a Radical Function

Warm-up: Graph the equation y = |x – 1|

SECTION 9-3 : SOLVING QUADRATIC EQUATIONS

Linear Equations Quadratic Equations Proportion Simultaneous Equations

Completing the square means writing the unknown terms of a quadratic in a square bracket Example because Application To find the maximum or minimum value.

Solve Systems of Linear Equations in Three Variables

Absolute Value inequalities

Solve Systems of Linear Inequalities

Objectives Solve quadratic equations by graphing or factoring.

6.5 Solving Inequalities by Factoring

Systems of Linear and Quadratic Equations

“Teach A Level Maths” Vol. 2: A2 Core Modules

Using Factoring To Solve

Solving Systems of Linear Inequalities

UNIT 6 REVIEW FOR GRAPHING INEQUALITIES TEST

Algebra 1B – Name: _________________________

Warm-Up 1) Sketch a graph of two lines that will never intersect.

INEQUALITIES Many Kinds of Inequalities : Linear Inequalities

3.5 Solving Nonlinear Systems

Factorise and solve the following:

Presentation transcript:

The Modulus Function Objectives: Understand what an absolute value is. Solve equations and inequalities involving modulus. Graph modulus functions.

The Modulus Function SUMMARY To solve inequalities involving one or more modulus functions:  Sketch the functions. ( Type “abs” if a graphical calculator is used. )  Find the points of intersection using the related functions ( without the mod. signs ). ( A negative sign is needed for reflected parts. )  Refer to the graph to write the inequality for x.  Mark the section(s) of the x -axis that give the solution. Method 1:

The Modulus Function SUMMARY Method 2:  Square both sides of the inequality to remove the mod. signs and solve the resulting linear or quadratic inequality. ( A graph is needed for quadratic inequalities. )

The Modulus Function 1. x y Exercise Solutions: Solve the inequalities. 1.2.

The Modulus Function 1. x y Exercise Solutions: Solve the inequalities By symmetry, Or:

The Modulus Function A xx B x y Solutions: 2. For B: By symmetry, at A: So, ( One region so one inequality ) (N.B. Strict inequality )

The Modulus Function Method 2: Zeros: So:

The Modulus Function Activity Card match pair up the cards to solve the inequalities

The Modulus Function A x x B x y Exercise Solution: 1. Solve the inequalities For B, 3 For A, or So,

The Modulus Function Method 2: So, Zeros:

The Modulus Function A B x x Exercise 2. Solution: For B, For A, or: So, ( Two regions so two inequalities )

The Modulus Function Zeros: Method 2: So,

The Modulus Function