Chapter 2.6: Rational Functions

Rational functions [R(x)] are any functions that can be written as

when both f(x) and g(x) are polynomials (Fraction = RATIO ; RATIOnal function, get it??)

Because R(x) is a fraction, there are some values for X and Y which make R(x) UNDEF

INED

These values are called ASYMPTOTES

On a graph, asymptotes appear as dotted lines where the graph does not cross

There are two types of asymptotes, Vertical (Y), and HORRIZONTAL (X)

any value that makes g(x) = ZERO is a VERTICAL ASYMPTOTE

Set g(x) = ZERO and solve for x (The solutions are -4 , 3)

When x is -4 or 3, g(x) = ZERO, and R(x) becomes UNDEFINED

X CANNOT be equal to -4 or 3

This creates VERTICAL asymptotes at X = -4 and X = 3

HORIZONTAL asymptotes are a little more tricky

3 rules:

1. Horizontal Asymptote (HA) is ZERO when the highest degree of the Numerator is SMALLER than the highest degree of the Denominator

ex: (5 > 2)

2. If Highest degree of numerator is BIGGER than the highest degree of the denominator,

There is NO horizontal asymptote

ex: 100 > 4 so there is NO Horizontal asymptote

3. If highest degrees of numerator and denominator are EQUAL,

HA = Coefficient of highest degree term in Numerator

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Coefficient of highest degree term in Denominator

ex:

4 / 2 = 2

HA = 2