Grade 12 · Mathematics
Rational functions
Why it matters
Asymptotes.
Advanced20m readingPrerequisite: Factor theorem
What is an asymptote of a rational function?
Short answer
An asymptote is a line that the graph of a rational function approaches but never reaches. A vertical asymptote occurs where the denominator is zero and the numerator is not, marking values the function cannot take. A horizontal asymptote describes the function’s end behaviour, determined by comparing the degrees of the numerator and denominator.
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Frequently asked questions
- Where is a vertical asymptote?
- At x-values that make the denominator zero while the numerator is non-zero, since the function is undefined there.
- How do you find a horizontal asymptote?
- Compare the degrees of numerator and denominator; the ratio of leading coefficients gives it when the degrees are equal.