Properties of Rational Functions Section 5.2 Properties of Rational Functions

OBJECTIVE 1

{ x | x ≠ -2 , x ≠ -6 } { x | x ≠ -4 } All Reals All Reals { x | x ≠ -2 }

OBJECTIVE 2

x = - 3 x = 2 and x = - 2 x = - 1 and x = - 4 x = 2

OBJECTIVE 3

A rational function R(x) is proper if the degree of the numerator is less than the degree of the denominator.

y = 0 is the horizontal asymptote Degree of numerator < degree of denominator y = 0 is the horizontal asymptote

A rational function R(x) is improper if the degree of the numerator is greater than or equal to the degree of the denominator.

2 Degree of numerator = degree of denominator , y = 2x2 /x2 = 2 y = 2 ___________________ Degree of numerator = degree of denominator , y = 2x2 /x2 = 2

Degree of numerator = degree of denominator , y = 5x6 /2x6 = 5/2

Vertical asymptotes: x = 1 and x = 1.19

x + 6 Oblique Asymptote is y = x + 6 ____________ __________ 13