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{{ printedBook.courseTrack.name }} {{ printedBook.name }} We are asked to draw the graph of $f(x)=-∣x+3∣−2.$ To do so, we will use a table of values to find points on the graph. Recall that the absolute value *removes* the negative sign. In this case, however, we have a negative sign preceding the absolute value. This will take each positive value created by the absolute value and then make it negative, regardless of its original sign.

$x$ | $-∣x+3∣−2$ | Simplify absolute value | $f(x)=-∣x+3∣−2$ |
---|---|---|---|

$-7$ | $-∣-7+3∣−2$ | $-(4)−2$ | $-6$ |

$-5$ | $-∣-5+3∣−2$ | $-(2)−2$ | $-4$ |

$-3$ | $-∣-3+3∣−2$ | $-(0)−2$ | $-2$ |

$-1$ | $-∣-1+3∣−2$ | $-(2)−2$ | $-4$ |

$1$ | $-∣1+3∣−2$ | $-(4)−2$ | $-6$ |

Now, we will plot and connect the obtained points. Doing that we keep in mind that the graph of an absolute value function has a V

shape.