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Asymptotes have many applications in higher level maths, including calculus in the study of continuity. While you could find the horizontal asymptotes by considering the end behavior of the function, we can also use the rules presented here that are based on the degree of the numerator and denominator. While the graph of a rational function will never cross a vertical asymptote, there are some circumstances in which it might cross a horizontal asymptote.
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Concept (1)
Sample Problems (12)
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Graphing a Rational Expression
Problem 1 3,742 viewsGraph:
f(x) = 1 + 2 x 
Graphing a Rational Expression
Problem 2 3,324 viewsGraph:
f(x) = 1 x + 3 
Graphing a Rational Expression
Problem 3 3,104 viewsGraph:
f(x) = 1 x 
Graphing a Rational Expression
Problem 4 373 views 
Graphing a Rational Expression
Problem 5 315 views 
Graphing a Rational Expression
Problem 6 298 views 
Graphing a Rational Expression
Problem 7 351 views 
Graphing a Rational Expression
Problem 8 316 views 
Graphing a Rational Expression
Problem 9 269 views 
Graphing a Rational Expression
Problem 10 286 views 
Graphing a Rational Expression
Problem 11 273 views 
Graphing a Rational Expression
Problem 12 243 views
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