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{{ printedBook.courseTrack.name }} {{ printedBook.name }} Recall that rational functions of the form $f(x)=x−ha +k$ can be called *simple rational functions*. In this form, $x=h$ is the vertical asymptote and $y=k$ is the horizontal asymptote. With this in mind, let's begin by determining the asymptotes of the given function.
$f(x)=x−ha +k→f(x)=x−1-2 +2 $
The vertical asymptote is $x=1$ and the horizontal asymptote is $y=2.$ To graph the function, we will first graph these asymptotes on the coordinate plane.

Next, we will make a table of values. To do so, we will consider $x-$values both to the left and to the right of the vertical asymptote.

$x$ | $x−1-2 +2$ | $f(x)$ |
---|---|---|

$-3$ | $-3−1-2 +2$ | $2.5$ |

$-1$ | $-1−1-2 +2$ | $3$ |

$0.5$ | $0.5−1-2 +2$ | $6$ |

$1.5$ | $1.5−1-2 +2$ | $-2$ |

$3$ | $3−1-2 +2$ | $1$ |

$5$ | $5−1-2 +2$ | $1.5$ |

Finally, we can plot the points $(x,f(x))$ on the same coordinate plane and connect them with smooth curves.