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 \(\displaystyle{y}\in{\left(—\infty,-{1}\right)}\cup{\left(-{1},\infty\right)}\)