Aim #18: How do we find holes and vertical asymptotes for
rational functions?
HW Packet Due Wednesday 10/26
Quiz(Aims 18-21) Wed. 10/26 AND Quarterly Fri/Mon 10/28 & 10/31
Do Now:
Find the domain of the following functions:
a.
c.
b.
Rational Functions:
A rational function is a function of the form:
where p and q are polynomial functions and q is not the
zero polynomial.
The domain of a rational function is the set of all real
numbers except those for which the denominator q is 0.
Answer the following:
Are the following two expressions equivalent?
?
Hole or Vertical Asymptote?
The first step to determining if a rational function has a hole or
vertical asymptote is to factor both the numerator and denominator
and simplify (if possible) .
If factors cancel out, then there is a hole at that zero.
So f(x) has a hole at (a, f(a)) *make sure to find the
y-coordinate*
If factors do NOT cancel, the factors remaining in the
denominator help us find the vertical asymptotes.
So f(x) has a vertical asymptote at x = b
Examples:
Hole:
Vertical Asymptote:
Determine all of the holes and vertical asymptotes of the
following rational functions.
Determine all of the holes and vertical asymptotes of the
following rational functions.
Determine the following for
Domain:
Holes:
Vertical Asymptotes:
Zeros:
Y-intercept:
Determine the following for
Domain:
Holes:
Vertical Asymptotes:
Zeros:
Y-intercept:
Determine the following for
Domain:
Holes:
Vertical Asymptotes:
Zeros:
Y-intercept: