Table of Contents Rational Functions: Slant Asymptotes Slant Asymptotes: A Slant asymptote of a...
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Transcript of Table of Contents Rational Functions: Slant Asymptotes Slant Asymptotes: A Slant asymptote of a...
Table of Contents
Rational Functions: Slant Asymptotes
Slant Asymptotes: A Slant asymptote of a rational function is a slant line (equation: y = mx + b) such that as values of the independent variable, x, decrease without bound or increase without bound, the function values (y-values) approach (get closer and closer to) the y-values of the points on the slant asymptote (from either above or below).
The next slide illustrates the definition.
Table of Contents
Rational Functions: Slant Asymptotes
Slide 2
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0
1
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-4 -3 -2 -1 1 2 3 4
slant asymptote (dashed line)
As x increases the y-values of points on the graph get closer to the y-values of points on the asymptote.
As x decreases the y-values of points on the graph get closer to the y-values of points on the asymptote.
Table of Contents
Rational Functions: Slant Asymptotes
Slide 3
Example: Find the slant asymptote of .12
3
x
xxf
Divide the numerator by the denominator using the "long division" process.
xx
xxx
3
32 1
- xThe slant asymptote is y = quotient.
slant asymptotey = x
(This was the function shown graphed in the preceding slide!)
Table of Contents
Rational Functions: Slant Asymptotes
Slide 4
Try: Find the slant asymptote of .1
32 2
xxx
xf
The slant asymptote is y = 2x + 3.
Table of Contents
Rational Functions: Slant Asymptotes