Inequalities of Combined Functions Example 1 TECHNIQUES FOR ILLUSTRATING INEQUALITIES.

Slides:

Advertisements

Similar presentations

Polynomial Inequalities in One Variable

Advertisements

Appendix B.4 Solving Inequalities Algebraically And Graphically.

Precalculus January 17, Solving equations algebraically Solve.

Area Between Two Curves 7.1. Area Formula If f and g are continuous functions on the interval [a, b], and if f(x) > g(x) for all x in [a, b], then the.

Essential Question: What is one important difference between solving equations and solving inequalities?

4-8 COMPOUND INEQUALITIES MISS BATTAGLIA – ALGEBRA 1 CP OBJECTIVE: SOLVE COMPOUND INEQUALITIES AND ABSOLUTE VALUE INEQUALITIES AND GRAPH THE SOLUTIONS.

Lesson 8.4 Inequalities Of Combined Functions

Finding the Inverse. 1 st example, begin with your function f(x) = 3x – 7 replace f(x) with y y = 3x - 7 Interchange x and y to find the inverse x = 3y.

Unit 1 Test Review Answers

Section 7.2a Area between curves.

Bellwork: Graph each line: 1. 3x – y = 6 2. Y = -1/2 x + 3 Y = -2

Compound Inequalities

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

SECTION 3.4 POLYNOMIAL AND RATIONAL INEQUALITIES POLYNOMIAL AND RATIONAL INEQUALITIES.

Lesson 4-2 Operations on Functions. We can do some basic operations on functions.

1 Solve each: 1. 5x – 7 > 8x |x – 5| < 2 3. x 2 – 9 > 0 :

Copyright © 2014, 2010, 2006 Pearson Education, Inc. 1 Chapter 2 Linear Functions and Equations.

Method of Graph sketching Solve the quadratic inequality x 2 – 5x + 6 > 0 graphically.

Further Pure 1 Lesson 8 – Inequalities. Wiltshire Inequalities Inequalities involve the relationships >,

Objectives Solve compound inequalities with one variable.

Review of 1.4 (Graphing) Compare the graph with.

Quadratic Inequalities You can solve a quadratic inequality algebraically by factoring. Just like solving a quadratic equality we set it = to 0. we move.

1. g(x) = -x g(x) = x 2 – 2 3. g(x)= 2 – 0.2x 4. g(x) = 2|x| – 2 5. g(x) = 2.2(x+ 2) 2 Algebra II 1.

Functions of Several Variables Copyright © Cengage Learning. All rights reserved.

 A polynomial inequality is an inequality that can take on 1 of 4 forms:  f(x) < 0  f(x) > 0  f(x) ≤ 0  f(x) ≥ 0  Here the function f(x) is a polynomial.

3.5 Polynomial and Rational Inequalities 1.Solve Polynomial Inequalities Algebraically and Graphically 2.Solve Rational Inequalities Algebraically and.

2.6 Families of Functions Sets of functions, called families, in what each function is a transformation of a special function called the parent. Linear.

Applications of Integration 7 Copyright © Cengage Learning. All rights reserved.

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.

Quadratic Inequalities First day: Review inequalities on number lines. Review inequalities of linear equations Review inequalities of systems of linear.

Do Now Draw the graph of: 2x – 4y > 12. Solving a system of Inequalities Consider the system x + y ≥ -1 -2x + y <

Mod 2.3: Solving Absolute Value Inequalities

Combinations of Functions

10.8 Systems of Second-Degree Equations and Inequalities

Notes Over 2.1 Graph the numbers on a number line. Then write two inequalities that compare the two numbers and and 9 l l l.

Calculus section 1.1 – 1.4 Review algebraic concepts

Pre-Algebra Chapter 7 Review

Absolute Value Functions

6-7 Graphing and Solving Quadratic Inequalities

Learning Target I can solve and graph multi-step, one-variable inequalities using algebraic properties.

Polynomial Inequalities in One Variable

Section 2.6 The Algebra of Functions

4.5 Polynomial and Rational Inequalities

Chapter 2: Analysis of Graphs of Functions

Operations on Functions

5.1 Combining Functions Perform arithmetic operations on functions

Inverse Relations & Square Root Functions

Functions Review.

Algebraic Expressions, Equations, and Symbols

Special Graphs of Inequalities.

Special Graphs of Inequalities.

Combinations of Functions

2-6: Combinations of Functions

2.5 Absolute Value Equations and Inequalities

Algebraic and Graphical Evaluation

Chapter 3 Graphs and Functions.

Finding the Total Area y= 2x +1 y= x Area = Area =

Solving absolute value equations visually

6-1: Operations on Functions (+ – x ÷)

Inverse Functions Inverse Functions.

Algebra 1B – Name: _________________________

1.5 Combination of Functions

Finding the Total Area y= 2x +1 y= x Area = Area =

Special Graphs of Inequalities.

Chapter 3 Graphs and Functions.

2-6: Combinations of Functions

f(x) g(x) x x (-8,5) (8,4) (8,3) (3,0) (-4,-1) (-7,-1) (3,-2) (0,-3)

Notes Over 6.1 Graphing a Linear Inequality Graph the inequality.

Bellwork Graph on a number line 1.) x < 4 2.) y ≥ -2 3.) x ≤ 0

Warm up – Solve the Quadratic

Presentation transcript:

Inequalities of Combined Functions Example 1 TECHNIQUES FOR ILLUSTRATING INEQUALITIES

Graphing to Identify P.O.I’s Let f(x) = x and g(x) = (x-2) 2

Graphing to Identify P.O.I From graphs we can see that P.O.I’s are (1,1) and (4,4) We can verify this algebraically:

Illustrating Graph Regions: Method 1 Compare the function visually Different colours represent different regions of graph Easy to visualize regions where one function is greater than the other

Analyze the Difference Function Subtract the functions and see where the graph of the difference is above the x-axis Illustrating Graph Regions: Method 2

Illustrating Graph Regions: Method 3 F(x) and g(x) can also be compared by analysing their quotient. Graph the combined function and identify the intervals for which This quotient is greater than one, which will correspond to where f(x) > g(x)

Conclusively, algebraic and graphical representations of inequalities can be useful for solving problems involving combined functions.