Vertical and horizontal asymptotes of rational functions
Find the vertical and horizontal asymptotes of a rational function from its equation. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
State the equation of the horizontal asymptote of the rational function.
f(x) = (−3x + 5)/(3x - 12)
Answer: y = -1
See one solved, step by step
State the equation of the horizontal asymptote of the rational function.
f(x) = (−3x + 3)/(x - 2)
📘 Worked solution
1Leading coefficient of the numerator: −3. Leading coefficient of the denominator: 1.Both the numerator and denominator are degree 1, so compare their leading coefficients.
2y = −31 = −3For equal-degree numerator and denominator, the horizontal asymptote is the ratio of the leading coefficients.
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