Rational functions/Examples/Sketch/Exercise

Sketch the graph of the following rational functions

$f=g/h\colon U\longrightarrow \mathbb {R} ,$

where each time ${}U$ is the complement set of the set of the zeros of the denominator polynomial ${}h$.

1. ${}1/x$,
2. ${}1/x^{2}$,
3. ${}1/(x^{2}+1)$,
4. ${}x/(x^{2}+1)$,
5. ${}x^{2}/(x^{2}+1)$,
6. ${}x^{3}/(x^{2}+1)$,
7. ${}(x-2)(x+2)(x+4)/(x-1)x(x+1)$.

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