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NYH
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How to state the equations of a rational functions with the following asymptotes?
(1)x=2, y=-3
(2)y=0, x=4
(3)y=0
(1)x=2, y=-3
(2)y=0, x=4
(3)y=0
Welcome NYH,NYH said:How to state the equations of a rational functions with the following asymptotes?
(1)x=2, y=-3
(2)y=0, x=4
(3)y=0
A rational function is a function that can be written as the ratio of two polynomials, where the denominator is not equal to zero.
Asymptotes are lines that a rational function approaches but never touches. They can be either horizontal or vertical.
To find the asymptotes of a rational function, set the denominator equal to zero and solve for the variable. The resulting values will be the vertical asymptotes. To find the horizontal asymptote, compare the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y=0. If the degrees are equal, the horizontal asymptote is the ratio of the leading coefficients of the numerator and denominator.
Yes, a rational function can have multiple asymptotes. It can have both vertical and horizontal asymptotes, and it can also have multiple of each type.
Yes, a rational function can have a slant or oblique asymptote when the degree of the numerator is exactly one more than the degree of the denominator. In this case, the slant asymptote is found by dividing the numerator by the denominator using long division.