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Jason
- Site Admin
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- Joined: Sun Dec 21, 2025 8:56 pm
The vertical asymptote is found by factoring the numerator and denominator as much as you can and then solving for x in the denominator.
ex. a
What is the vertical asymptote, if any?
\(y = \dfrac{4x^{2} - 1}{3x(2x + 1)}\)
\(y = \dfrac{(2x - 1)(2x + 1)}{3x(2x + 1)}\)
\(y = \dfrac{2x - 1}{3x}\)
\(3x = 0\)
\(\dfrac{3}{3}x = \dfrac{0}{3}\)
\(x = 0\)
\(0\) is the vertical asymptote
ex. b
What is the vertical asymptote, if any?
\(\dfrac{4}{9}x^{2} - \dfrac{3}{7}\)
There is no vertical asymptote, because no x in the denominator.
