2.8. Zeroes of Rational Functions http://www.ck12.org
2.8 Zeroes of Rational Functions
Here you will revisit how to find zeroes of functions by focusing on rational expressions and what to do in special
cases where the zeroes and holes seem to overlap.
The zeroes of a function are the collection ofxvalues where the height of the function is zero. How do you find
these values for a rational function and what happens if the zero turns out to be a hole?
Watch This
Focus on the portion of this video discussing holes andx-intercepts.
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/60830http://www.youtube.com/watch?v=UnVZs2EaEjI James Sousa: Find the Intercepts, Asymptotes, and Hole of a
Rational Function
Guidance
Zeroes are also known asx-intercepts, solutions or roots of functions. They are thexvalues where the height of the
function is zero. For rational functions, you need to set the numerator of the function equal to zero and solve for the
possiblexvalues. If a hole occurs on thexvalue, then it is not considered a zero because the function is not truly
defined at that point.
Example A
Identify the zeroes and holes of the following rational function.
f(x) =(x−^1 )(xx++^33 )(x+^3 )
Solution: Notice how one of thex+3 factors seems to cancel and indicate a removable discontinuity. Even though
there are twox+3 factors, the only zero occurs atx=1 and the hole occurs at (-3, 0).