Name ________________________________________________________ Date _______________________ 9-3 Rational Functions (& their graphs) A rational function is one that has polynomials in the numerator and the denominator. A point of discontinuity is an X-VALUE that would make the denominator zero. (Remember, in math world, really really bad things happen when you divide by zero.) To FIND a point of discontinuity, you’re going to ____________________________________. Example 1... For each rational function, find any points of discontinuity. (Hint: factor!) a. b. A point of discontinuity can be one of two different types: 1. A hole – factor cancels out 2. A vertical asymptote – factor doesn’t cancel out Example 2... Describe the vertical asymptotes and/or holes for the graph of each rational function. (Hint: first, find points of discontinuity. Then decide which kind they are.) a. b. c. d.
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Name ________________________________________________________ Date _______________________
9-3 Rational Functions (& their graphs)
A rational function is one that has polynomials in the numerator and the denominator.
A point of discontinuity is an X-VALUE that would make the denominator zero. (Remember,
in math world, really really bad things happen when you divide by zero.)
To FIND a point of discontinuity, you’re going to ____________________________________.
Example 1... For each rational function, find any points of discontinuity. (Hint: factor!)
a. b.
A point of discontinuity can be one of two different types:
1. A hole – factor cancels out 2. A vertical asymptote – factor doesn’t cancel out
Example 2... Describe the vertical asymptotes and/or holes for the graph of each
rational function. (Hint: first, find points of discontinuity. Then decide which kind they are.) a. b.
c. d.
Horizontal asymptotes have a different set of rules.
Rule #1: If the degree of denominator > degree of numerator, that means there’s a
horizontal asymptote at y=o.
Rule #2: If the degree of numerator > degree of denominator, that means there is
no horiztonal asymptote.
Rule #3: If the degrees are the same, that means there’s a horizontal asymptote at
the ratio of leading coefficients.
Remember, BOBO BOTN EATS DC!
Bigger On Bottom, 0; Bigger On Top, None; Exponents Are The Same, Divide Coefficients
Example 3... Find the horizontal asymptote of the graph of each rational function.
a. b. c.
When we put all of that information (holes, vertical asymptotes, horizontal asymptotes)
together, we can get an idea of what the graph of a rational function looks like.
Example 4... Sketch the graph of each function.
a. b.
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