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{{ printedBook.courseTrack.name }} {{ printedBook.name }} Note that the given rational function is written in the form $g(x)=b(x−h)1 +k.$ Let's identify the transformations that the values of $b,$ $h,$ and $k$ produce.

Constant | Condition | Transformation |
---|---|---|

$b$ | $1<b$ | Horizontal shrink by a factor of $b$ |

$0<b<1$ | Horizontal stretch by a factor of $b$ | |

$h$ | $h<0$ | Horizontal translation left $h$ units |

$h>0$ | Horizontal translation right $h$ units | |

$k$ | $k<0$ | Vertical translation down $k$ units |

$k>0$ | Vertical translation up $k$ units |

Let's now identify the constants in the given function rule.
$g(x)=2(x−3)1 +1⇔g(x)=2(x−3)1 +1 $
We can see that $b$ $=$ $21 ,$ $h$ $=$ $3,$ and $k$ $=$ $1.$
Therefore, the transformations of the parent function that result in the graph of the given function are a horizontal shrunk by a factor of $21 ,$ followed by a translation $3$ units right and $1$ unit up. These correspond to choices **B**, **E**, and **G**.