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{{ printedBook.courseTrack.name }} {{ printedBook.name }} Let's graph $t(x)$ first and then we can compare it to the graph of the parent function $f(x).$

To graph the function, let's make a table of values first!

$x$ | $∣x∣+21 $ | Simplify | $t(x)$ |
---|---|---|---|

$-5$ | $∣-5∣+21 $ | $5+0.5$ | $5.5$ |

$-3$ | $∣-3∣+21 $ | $3+0.5$ | $3.5$ |

$-1$ | $∣-1∣+21 $ | $1+0.5$ | $1.5$ |

$0$ | $∣0∣+21 $ | $0+0.5$ | $0.5$ |

$1$ | $∣1∣+21 $ | $1+0.5$ | $1.5$ |

$3$ | $∣3∣+21 $ | $3+0.5$ | $3.5$ |

$5$ | $∣5∣+21 $ | $5+0.5$ | $5.5$ |

Now we can plot these ordered pairs on a coordinate plane and connect them to get the graph of $t(x).$ Notice that $t(x)$ is a transformation of $f(x)$ and the graph of $f(x)=∣x∣$ is V-shaped. Thus, $t(x)$ will also be a V-shaped graph.

To compare our graph to the graph $f(x)=∣x∣,$ let's draw them on one coordinate plane.

As we can see, the graph of $t(x)$ is a vertical translation $0.5$ units up of the graph $f(x).$