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Math Help - Rational Functions

  1. #1
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    Rational Functions

    Hi,
    If you were given, say: x-intercept of -4, y-intercept of -2, vertical asymptote x=2, and horizontal asymptote y=1. How do you find the equation for a rational function with these features?
    Thanks in advance.
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  2. #2
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    Quote Originally Posted by Hellooo View Post
    Hi,
    If you were given, say: x-intercept of -4, (x+4) in the numerator

    y-intercept of -2, y = -2 when x = 0

    vertical asymptote x=2, (x-2) in the denominator

    and horizontal asymptote y=1. degree of numerator = degree of denominator and ratio of the leading coefficients = 1

    y = \frac{x+4}{x-2}
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  3. #3
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    Thanks, but can you show the steps in how you reached the answer?
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  4. #4
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    Quote Originally Posted by Hellooo View Post
    Hi,
    If you were given, say: x-intercept of -4, y-intercept of -2, vertical asymptote x=2, and horizontal asymptote y=1. How do you find the equation for a rational function with these features?
    Thanks in advance.
    The simplest model to use is y = \frac{a}{x - b} + c. Your job is to find the values of a, b and c using the given information. You will get an answer equivalent to skeeter's.

    In fact, the only information required is vertical asymptote x=2, horizontal asymptote y=1 and y-intercept of -2. The information x-intercept of -4 can be used to check your answer.
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  5. #5
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    Quote Originally Posted by Hellooo View Post
    Thanks, but can you show the steps in how you reached the answer?
    To supplement to Mr. Fantastic's information: horizontal asymptotes occur in the numerator and vertical asymptotes occur in denominator. If you recall a function cannot cross an asymptote (always in the case of vertical, most times true in the case of horizontal). Which means that the function cannot be a certain value there.

    Thus, if a vertical asymptote of 2 exists we must have (x - 2) in the denominator.

    Also recall that at the x-intercept y = 0, thus we must have (x+4) in the numerator because our x-intercept of -4 makes this equation 0.
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