Rational Expressions and Functions

1. Rational Expressions and Functions Chapter 11

2. 11.1 Simplifying Rational Expressions • Pg. 664 – 669 • Obj: learn how to simplify rational expressions. • Content Standard: Prepares for A.APR.7

3. 11.1 Simplifying Rational Expressions • Rational expression – an expression that has polynomials in the numerator and the denominator • Excluded Value – a value of a variable for which a rational expression is undefined

4. 11.2 Multiplying and Dividing Rational Expressions • Pg. 670 – 676 • Obj: Learn how to multiply and divide rational expressions and simplify complex fractions. • Content Standard: A.APR.7

5. 11.2 Multiplying and Dividing Rational Expressions • Multiplying Rational Expressions • Factor polynomials where necessary • Cancel where possible • Multiply numerators; multiply denominators • Simplify if necessary • Dividing Rational Expressions • Change multiplication to division and flip the second fraction • Follow multiplication rules

6. 11.2 Multiplying and Dividing Rational Expressions • Complex Fraction – a fraction that contains one or more fractions in its numerator, in its denominator, or both

7. 11.3 Dividing Polynomials • Pg. 678 – 683 • Obj: Learn how to divide polynomials. • Content Standard: A.APR.6

8. 11.3 Dividing Polynomials • Dividing a Polynomial by a Polynomial • Arrange the terms of the dividend and divisor in standard form. If a term is missing from the dividend, add the term with a coefficient of 0. • Divide the first term of the dividend by the first term of the divisor. This is the first term of the quotient • Multiply the first term of the quotient by the whole divisor and place the product under the dividend. • Subtract this product from the dividend. • Bring down the next term. • Repeat the process.

9. 11.4 Adding and Subtracting Rational Expressions • Pg. 684 – 689 • Obj: Learn how to add and subtract rational expressions. • Content Standard: A.APR.7

10. 11.5 Solving Rational Equations • Pg. 691 – 697 • Obj: Learn how to solve rational equations and proportions. • Content Standards: A.CED.1 and A.REI.2

11. 11.5 Solving Rational Equations • Rational Equation – an equation that contains one or more rational expressions • Method • Find the LCD • Multiply both sides of the equation by the LCD • Solve the equation • Check for extraneous solutions

12. 11.6 Inverse Variation • Pg. 698 – 704 • Obj: Learn how to write and graph equations for inverse variations and compare direct and inverse variations. • Content Standards: F.IF.5 and A.CED.2

13. 11.6 Inverse Variation • Inverse Variation – xy=k • Constant of Variation for an Inverse Variation - k

14. 11.7 Graphing Rational Functions • Pg. 705 – 712 • Obj: Learn how to graph rational functions. • Content Standards: F.IF.4 and A.CED.2

15. 11.7 Graphing Rational Functions • Rational Function – can be written in the form f(x) = polynomial/polynomial, where the denominator cannot be 0 • Asymptote – a line that the graph gets closer to, but never crosses • Identifying Asymptotes • Vertical Asymptote: x=b • Horizontal Asymptote: y=c

16. 11.7 Graphing Rational Functions • Families of Functions • Linear Function y=mx + b • Parent function y = x • m = slope • b = y-intercept • Quadratic Function • Parent function y=x² • Axis of symmetry x=-b/2a • The greatest exponent is 2

17. 11.7 Graphing Rational Functions • Families of Functions • Absolute Value Function y=|x-a|+b • Parent Function y = |x| • Shift y=|x| horizontally a units • Shift y=|x| vertically b units • Vertex at (a,b) • Greatest Exponent is 1

18. 11.7 Graphing Rational Functions • Families of Functions • Exponential Function y=ab² • Growth where b>1 • Decay where 0<b<1 • The variable is the exponent • Square Root Function • Shift y=√x horizontally b units • Shift y=√x vertically c units • The variable is under the radical

19. 11.7 Graphing Rational Functions • Families of Functions • Rational Function • Vertical Asymptote at x=b • Horizontal Asymptote at y=c • The variable is in the denominator