Math Problem Statement
Find the horizontal and vertical asymptotes of the curve. You may want to use a graphing calculator (or computer) to check your work by graphing the curve and estimating the asymptotes. (Enter your answers as comma-separated lists. If an answer does not exist, enter DNE.)
y =
x3 − x
x2 − 4x + 3 x=
1,3 y=
x+4
Solution
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Math Problem Analysis
Mathematical Concepts
Rational Functions
Asymptotes
Polynomial Long Division
Formulas
To find vertical asymptotes, solve denominator = 0
Horizontal asymptotes are determined by comparing degrees of numerator and denominator
Polynomial long division to find slant asymptote
Theorems
Degree rule for asymptotes (horizontal vs slant)
Polynomial long division for slant asymptotes
Suitable Grade Level
Grades 11-12
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