Give the range of the rational functions given that neither of the graphs crosses its horizontal asymptote. Write your answers in set notation and int

sagnuhh 2021-06-27 Answered
Give the range of the rational functions given that neither of the graphs crosses its horizontal asymptote. Write your answers in set notation and interval notation.
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Nathanael Webber
Answered 2021-06-28 Author has 117 answers

1. For a rational function, the range is all real numbers, except the y values that correspond to holes or horizontal asymptotes.
In Example B, part(b), the horizontal asymptote was y=2. Therefore, the range is all real numbers, except y=2
The set notation for the range is {yRyq2}
The interval notation is y(,2)(2,)
2. In ‘Try These B, part(a), we were given
y=2xx+4
In a rational function, if the degree of the numerator and the denominator are the same, then the horizontal asymptote is given by
y= (ratio of the leading coefficients in the numerator/denominator)
In this case, we have
y=11=1
Therefore, the set notation for the range is y¢R|y1
The interval notation is y(,1)(1,)

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