asked in category: General Last Updated: 29th May, 2020

# How do you find vertical and horizontal asymptotes?

To find the vertical asymptote(s) of a rational function, we set the denominator equal to 0 and solve for x. The horizontal asymptote is a horizontal line which the graph of the function approaches but never crosses (though they sometimes cross them).

Similarly one may ask, how do you find a horizontal asymptote?

To find horizontal asymptotes:

1. If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0).
2. If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote.

Similarly, what is the horizontal asymptote? A horizontal asymptote is a y-value on a graph which a function approaches but does not actually reach. Here is a simple graphical example where the graphed function approaches, but never quite reaches, y=0 .

Consequently, what are the rules for horizontal asymptotes?

The three rules that horizontal asymptotes follow are based on the degree of the numerator, n, and the degree of the denominator, m.

• If n < m, the horizontal asymptote is y = 0.
• If n = m, the horizontal asymptote is y = a/b.
• If n > m, there is no horizontal asymptote.

What does vertical and horizontal asymptotes mean?

Horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to +∞ or −∞. As the name indicates they are parallel to the x-axis. Vertical asymptotes are vertical lines (perpendicular to the x-axis) near which the function grows without bound.

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29th May, 2020

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