Is it possible to have 2 horizontal asymptotes

On the left, the graph of a typical exponential function has one horizontal asymptote. In other words, as you trace your finger on the graph as far to the left as you can go, the y -coordinates seem to settle on the value The graph on the right shows a typical rational function. Tracing the graph either to the left or right, the y -coordinates approach a value of 1 in this example. Ok, so what kinds of functions have two horizontal asymptotes? Often when there is a radical involved as part of a fraction of two functions, then a second horizontal asymptote may appear.

These are quite challenging to analyze simply from the expression of the function you really need a good understanding of infinite limits to break these apart , so I recommend just looking at the graph whenever possible. Certain kinds of functions always have a specific number of asymptotes, so it pays to learn the classification of functions as polynomial, exponential, rational, and others.

More challenging problems may require working out infinite limits or carefully graphing the function. A little knowledge goes a long way on the AP Calculus exam! In addition, Shaun earned a B. Shaun still loves music -- almost as much as math! Shaun has taught and tutored students in mathematics for about a decade, and hopes his experience can help you to succeed!

View all posts. Click here to learn more! Active 2 years, 1 month ago. Viewed 29k times. Ilmari Karonen Kip Kip 1 1 gold badge 5 5 silver badges 12 12 bronze badges. As a matter of fact, the integral of any "bell-shaped" curve will have sigmoidal behavior. Add a comment. Active Oldest Votes. Isaac Isaac Vary it appropriately for additional constraints.

But that's okay; all I need to find is whichever term has the largest exponent. It doesn't matter where, within the expression, that term is located. So I know that this function's graph will have a horizontal asymptote which is the value of the division of the coefficients of the terms with the highest powers.

Those coefficients are 4 and —3. Then my answer is:. The highest power in the numerator is 2. There is an x 2 in the denominator, but that doesn't matter, because the highest power in the denominator is 5. Since the largest power underneath is bigger than the largest power on top, then the horizontal asymptote will be the horizontal axis.

Page 1 Page 2 Page 3 Page 4. All right reserved. Web Design by. Skip to main content. Purplemath Whereas vertical asymptotes are sacred ground, horizontal asymptotes are just useful suggestions. Content Continues Below. Does a table of values bear this out?

The numerator has degree 2, while the denominator has degree 3. A rational function will have a y -intercept when the input is zero, if the function is defined at zero. A rational function will not have a y -intercept if the function is not defined at zero.

Likewise, a rational function will have x -intercepts at the inputs that cause the output to be zero. Then, find the x — and y -intercepts and the horizontal and vertical asymptotes. Skip to main content. Rational Functions. Search for:.