 # 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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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 $\left\{y\in R\mid y\ne {q}_{2}\right\}$
The interval notation is $y\in \left(—\mathrm{\infty },2\right)\cup \left(2,\mathrm{\infty }\right)$
2. In ‘Try These B, part(a), we were given
$y=\frac{2-x}{x+4}$
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
$y=\frac{-1}{1}=-1$
Therefore, the set notation for the range is $y¢R|y-1$
The interval notation is $y\in \left(—\mathrm{\infty },-1\right)\cup \left(-1,\mathrm{\infty }\right)$