 Pg. 664 – 669  Obj: learn how to simplify rational expressions.  Content Standard: Prepares for A.APR.7

 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

 Pg. 670 – 676  Obj: Learn how to multiply and divide rational expressions and simplify complex fractions.  Content Standard: A.APR.7

 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

 Complex Fraction – a fraction that contains one or more fractions in its numerator, in its denominator, or both

 Pg. 678 – 683  Obj: Learn how to divide polynomials.  Content Standard: A.APR.6

 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.

 Pg. 684 – 689  Obj: Learn how to add and subtract rational expressions.  Content Standard: A.APR.7

 Pg. 691 – 697  Obj: Learn how to solve rational equations and proportions.  Content Standards: A.CED.1 and A.REI.2

 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

 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

 Inverse Variation – xy=k  Constant of Variation for an Inverse Variation - k

 Pg. 705 – 712  Obj: Learn how to graph rational functions.  Content Standards: F.IF.4 and A.CED.2

 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

 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

 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

 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

 Families of Functions › Rational Function  Vertical Asymptote at x=b  Horizontal Asymptote at y=c  The variable is in the denominator