1. Properties of Rational Functions
Section 5.2
Properties of Rational Functions

3. OBJECTIVE 1

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

13. OBJECTIVE 2

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

17. OBJECTIVE 3

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

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

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

21. 2 Degree of numerator = degree of denominator , y = 2x2 /x2 = 2 y = 2
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Degree of numerator = degree of denominator , y = 2x2 /x2 = 2

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

23. Vertical asymptotes:
x = 1 and x = 1.19

24. x + 6
Oblique Asymptote is y = x + 6
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