Find the slant (oblique) asymptote of a rational function.
Polynomial Coefficients
Numerator (ax² + bx + c)
Denominator (dx + e)
Asymptote Analysis
y = 1.00x + 5.00
Asymptote Equation
The linear function the graph approaches as x goes to infinity.
Slope (m)1.000
Y-intercept (c)5.000
Scale: 1 unit = 20px
Quick Reference
Numerator Degree2
Denominator Degree1
What is a Slant Asymptote?
A slant (or oblique) asymptote occurs when the degree of the numerator of a rational function is exactly one greater than the degree of the denominator. It represents a line that the graph of the function approaches as x approaches positive or negative infinity.
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Pro Tips
Slant asymptotes only exist if degree(numerator) = degree(denominator) + 1.
They are found by performing long division and ignoring the remainder.
Graphing the function alongside the asymptote line can help visualize the behavior.
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Fun Facts
"Rational functions never have both a horizontal and a slant asymptote simultaneously."
"The term 'asymptote' comes from the Greek word 'asymptotos', meaning 'not falling together'."
"Calculus students use limits to formally prove the existence of these lines."
Formula: y = mx + c (Result of Polynomial Long Division)
