Transcript File
Algebra 2B Chapter 9 Lesson 9.1 Learning Targets: • I can simplify Rational Expressions • I can simplify complex fractions Vocabulary Rational Expression: It’s the ratio of two polynomial expressions Examples: Complex Fraction: It’s a rational expression whose numerator and/or denominator contains a rational expression. Examples: Multiplying Rational Expressions: Dividing Rational Expressions: Review: How to multiply and divide monomials: How to multiply, divide and find the power of a power: How to factor polynomials: Summary of Factoring Techniques For all polynomials, first factor out the greatest common factor (GCF). For a binomial, check to see if it is any of the following: a.difference of squares: x2 − y2 = ( x + y) ( x − y) b.difference of cubes: x3 − y3 = ( x − y) ( x2 + xy + y2) c.sum of cubes: x3 + y3 = ( x + y) ( x2 − xy + y2) For a trinomial, use the T ax2 + bx + c: Step1: Factor the numerator and denominator completely 2 Step 2: Reduce any common factors Step 3: Simplify Step1: Factor the numerator and denominator completely 2 Step 2: Reduce any common factors Step 3: Simplify Step1: Make into a multiplication problem Step2: Factor the numerator and denominator completely Step 3: Reduce any common factors Step 4: Simplify Step1: Make into a multiplication problem Step2: Factor the numerator and denominator completely 3 Step 3: Reduce any common factors Step 4: Simplify 2 2 Closure 9.1(in class): Click the mouse button or press the Space Bar to display the answers. Lesson 9.2 Learning Targets : • I can determine the LCM of polynomials • I can add and subtract rational expressions Vocabulary To add and subtract Rational Expressions: To find equivalent fractions with the same denominator, we need the LCM. Your Turn: Your Turn: Your Turn: Your Turn: Closure Lesson 9.2 (in class): Click the mouse button or press the Space Bar to display the answers. Lesson 9.6 Learning Targets : I can solve Rational Equations Vocabulary A rational equation is ____________________________________________ ____________________________________________________________ Hint: When solving a rational equation, eliminate the fractions first! Check the solutions in the original equation Warm-up 9.3 4. 5. Lesson 9.3 Learning Targets : • I can determine the Vertical Asymptotes and the Point of Discontinuity (Hole) • I can graph Rational Functions Vocabulary Continuity:_________________________________________________ _________________________________________________________ To find the asymptote(s) and/or hole(s) of a rational function, we look at its denominator. Asymptote(s): ________________________ Hole(s): _____________________________ In your own words, vertical asymptote: _______________________________________________ _______________________________________________ hole: _______________________________________________ _______________________________________________ x f(x) Asymptote(s): ________________________ Hole(s): _____________________________ x Asymptote(s): ________________________ Hole(s): _____________________________ f(x) x Asymptote(s): ________________________ Hole(s): _____________________________ f(x) Use your graphing calculator to get the table of values. Asymptote(s): ________________________ Hole(s): _____________________________ Asymptote(s): ________________ Hole(s): _____________________ Asymptote(s): _______________ Hole(s): ____________________ Click the mouse button or press the Space Bar to display the answers. Warm-up 9.4: on the back of closure Asymptote: ____________ Asymptote: ____________ Hole: _________________ Hole: _________________ Simplify: 3. 4. Warm-up 9.4 Simplify: 3. 4. Lesson 9.4 Learning Targets : • I can recognize and solve direct and joint variation problems • I can recognize and solve inverse variation problems Vocabulary Examples: Examples: Closure Lesson 9.4 (in class): Click the mouse button or press the Space Bar to display the answers. Lesson 9.5 Learning Targets : • I can identify graphs as different types of functions • I can identify equations as different types of functions Use your Family Functions Cheat sheet to identify the functions represented by each graph. ________________________ __________________________ ______________________ _______________________ _______________________ _________________________ ________________________ __________________________ Click the mouse button or press the Space Bar to display the answers. Today, you must do in class: 1. Study guide & Review 2. Practice test (Multiple choice) Homework: Practice test from book (worksheet available) Click the mouse button or press the Space Bar to display the answers.