Section+2.6

Rational Functions: r(x)= p(x) / q(x) q(x) cannot equal 0 where p(x) and q(x) are polynomial functions
 * Graphs of Rational Functions:**

Domain: all real #'s except the values of x that would make the denominator = 0 ex. Find the domain f(x)= 1/ x-2 D- {2}

End Behavior: lim x-> 2- = - infinity as values get closer to 2 from the left the graph goes towards negative infinity lim x -> 2+ = infinity as values get closer to 2 from the right the graph goes towards infinity

Vertical Asymptote: x=a is a vertical asymptote of the function f(x) if lim x-> a- f(x) = + or - infinity or if lim x-> a+ f(x)= + or - inifinity

Asymptote Rules:

1) A vertical asymptote occurs at the values that make the denominator = 0

2) If the degree of p(x) < the degree of q(x) than y = 0 is a horizontal asymptote

3) If the degree of p(x) = the degree of q(x) than the ratio of the leading coefficients is a horizontal asymptote.

4) If the degree of p(x) > q(x) than the quotient of the function (ignoring the remainder) is an asymptote. If the degree of p(x) is exactly 1 more than q(x) than we get a __slant__ asymptote.

Standardized test questions: pg 245-246

63. False, 1/(x^2 + 1) is an example of this. 64. True 65.E 66.A 67.D 68. Degree of 8 lim x -> -2+ f(x)= infinity lim x -> -2 - f(x)= infinity.