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