RATIONAL FUNCTIONS 2.6. RATIONAL FUNCTIONS VERTICAL ASYMPTOTES  To find vertical asymptotes first reduce the function if possible.  Set the denominator.

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Presentation transcript:

RATIONAL FUNCTIONS 2.6

RATIONAL FUNCTIONS

VERTICAL ASYMPTOTES  To find vertical asymptotes first reduce the function if possible.  Set the denominator equal to zero and solve for x  Those are your asymptotes  Any factors that cancel are a “hole” in the graph.

FIND ALL VERTICAL ASYMPTOTES

HORIZONTAL ASYMPTOTES  n is the degree of N(x)  m is the degree of D(x)  If n<m y = 0 is a horizontal asymptote  If n>m there are no horizontal asymptotes  If n=m y=a/b is the horizontal asymptote where a is the leading coefficient of N(x) and b is the coefficient of D(x)

FIND ALL ASYMPTOTES AND IDENTIFY THE DOMAIN

FIND ALL ASYMPTOTES AND NAME THE DOMAIN

TWO DIFFERENT HORIZONTAL ASYMPTOTES

FIND THE ZEROS OF THE FUNCTION

HOMEWORK  Pg 148 #7-21 odd, 31 – 34 all