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{{ printedBook.courseTrack.name }} {{ printedBook.name }} Let's graph the function by ourselves to determine the error and correct it. The function is in the form of $y=x−ha +k$ where $x=h$ and $y=k$ are the asymptotes. Therefore, the asymptotes of the given function are $x=1$ and $y=-2.$ $y=x−12 −2 $ Looking at the given graph, we see that the vertical asymptote was determined wrongly. Next, we will make a table of values for the given function.

$x$ | $x−12 −2$ | $y$ |
---|---|---|

$-3$ | $-3−12 −2$ | $-2.5$ |

$-1$ | $-1−12 −2$ | $-3$ |

$-0.5$ | $-0.5−12 −2$ | $-6$ |

$1$ | $1−12 −2$ | Asymptote |

$1.5$ | $1.5−12 −2$ | $2$ |

$3$ | $3−12 −2$ | $-1$ |

$5$ | $5−12 −2$ | $-1.5$ |

Next, we will plot the points and draw two branches of the hyperbola so that they pass through the plotted points and approaches the asymptotes.

By comparing the graphs, we see the error clearly. $Correct$

$Wrong$