In Exercises 37–44, find the horizontal asymptote, if there is on...

Question

In Exercises 37–44, find the horizontal asymptote, if there is one, of the graph of each rational function. f(x)=12x/(3x^2+1)

Accepted Answer

for the given rational function. Find out the question of the horizontal asking toe. Our equation says we have five x over two X squared plus seven. Now to find what our asientos, we're gonna look at the degrees in our polynomial. In fact the elected degrees of our leading term. So in this case on the top we just have five X. So you look at the degree of five X. We have X to the first. So do we have the numerator is equal to what? On the bottom? Our leading term is two X squared. The degree for that one is R squared which is two. Now there are a couple of rules for horizontal institutes. If a degree in is less than a degree D R a cento is Y equals zero. If it is equal to D. We got some top is the ratio of leading coefficients. And finally, if n is greater than the There is no horizontal sm two and we have to do a little bit more work to determine if there is a slant. As in Tokyo. But in this case we just want to find a horizontal. Well if you look here We have in this one di is 21 is less than two, meaning that are a cento is white gold zero machines. The answer is the answer. A Okay I hope to help you solve the problem. Thank you for watching. Goodbye

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In Exercises 37–44, find the horizontal asymptote, if there is one, of the graph of each rational function. f(x)=12x/(3x^2+1)

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