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jann95
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I just got this assignment for math and the question was is it possible to have a cubic asymptote in a rational function. If so explain how and where.
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jann95 said:I just got this assignment for math and the question was is it possible to have a cubic asymptote in a rational function. If so explain how and where.
jann95 said:A quadratic asymptote is an asymptote on a rational function which looks like a parabola. So if you are graphing a rational function with a quadratic asymptote is doesn't pass through. Just like the oblique, vertical and horizontal asymptotes.
Mark44 said:I haven't run across this term (cubic asymptote) before, but I would guess that it means that for large |x|, the graph approaches that of some cubic polynomial.
No, and asymptote does NOT have to be a straight line. Any curve can be an asymptote to a graph. The only requirement is that the graph, as x-> a, must get arbitrarily close to the curve without reaching it.LCKurtz said:Asymptotes don't "look like parabolas". They are straight lines. And I am certain your text doesn't define a quadratic asymptote as one that "looks like a parabola". Tell me, word for word, what your text definition of a quadratic asymptote is. How can you hope to solve a problem if you don't know the definitions?
HallsofIvy said:No, and asymptote does NOT have to be a straight line. Any curve can be an asymptote to a graph. The only requirement is that the graph, as x-> a, must get arbitrarily close to the curve without reaching it.
Cubic asymptotes are vertical lines that a rational function approaches as the input variable approaches infinity or negative infinity. They are also known as vertical asymptotes and are typically represented by the equation x = a, where a is a constant.
To find the cubic asymptotes of a rational function, you can use the following steps:
Rational functions have cubic asymptotes when the degree of the denominator is exactly three more than the degree of the numerator. This means that the highest power of x in the denominator is one degree higher than the highest power of x in the numerator.
Yes, it is possible for a rational function to have more than one cubic asymptote. This occurs when the degree of the numerator is less than the degree of the denominator, and there are multiple terms with the same highest power of x in the denominator.
Cubic asymptotes do not intersect or touch the graph of a rational function, but they do affect its behavior. As the input variable approaches infinity or negative infinity, the function will get closer and closer to the cubic asymptote, but will never actually reach it. The presence of a cubic asymptote also creates a break in the graph of the rational function at the point of the vertical line.