Vertical & horizontal asymptotes
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Flip to reveal answersWhere are the vertical asymptotes of a rational function?
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All 8 Flashcards — Vertical & horizontal asymptotes
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Question
Where are the vertical asymptotes of a rational function?
Answer
Where the denominator = 0 (and the numerator isn't also 0 there).
Question
How do you find the horizontal asymptote?
Answer
Compare degrees: top < bottom → y = 0; equal → y = (ratio of leading coefficients).
Question
What if top degree < bottom degree?
Answer
The horizontal asymptote is y = 0.
Question
What if top and bottom have equal degree?
Answer
y = (leading coefficient of top) ÷ (leading coefficient of bottom).
Question
Vertical asymptotes of (2x+1)/(x² − x − 6)?
Answer
x = 3 and x = −2 (from (x − 3)(x + 2) = 0).
Question
Horizontal asymptote of (4x − 3)/(2x + 1)?
Answer
y = 2 (equal degrees, 4/2).
Question
What happens if numerator and denominator are both 0 at x = a?
Answer
There's a hole at x = a, not a vertical asymptote (the factor cancels).
Question
What if the top degree is one MORE than the bottom?
Answer
There's a slant (oblique) asymptote instead of a horizontal one.
Read the notes
Full study notes for Vertical & horizontal asymptotes
Topic 2.13 hub
Rational functions (HL only)
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