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$y=∣x+6∣−4$

Substitute$x=-10$

$y=∣-10+6∣−4$

AddTermsAdd terms

$y=∣-4∣−4$

AbsNeg$∣-4∣=4$

$y=4−4$

SubTermSubtract term

$y=0$

$x$ | $∣x+6∣−4$ | $y$ |
---|---|---|

$-10$ | $∣-10+6∣−4$ | $0$ |

$-8$ | $∣-8+6∣−4$ | $-2$ |

$-6$ | $∣-6+6∣−4$ | $-4$ |

$-4$ | $∣-4+6∣−4$ | $-2$ |

$-2$ | $∣-2+6∣−4$ | $0$ |

$0$ | $∣0+6∣−4$ | $2$ |

$2$ | $∣2+6∣−4$ | $4$ |

$4$ | $∣4+6∣−4$ | $6$ |

To draw the graph, we will plot and connect the obtained points. Do not forget that the graph of an absolute value function has a V

-shape!

The graph given in option **C** is the graph of the function.

b

$x$ | $∣x−6∣−4$ | $y$ |
---|---|---|

$-4$ | $∣-4−6∣−4$ | $6$ |

$-2$ | $∣-2−6∣−4$ | $4$ |

$0$ | $∣0−6∣−4$ | $2$ |

$2$ | $∣2−6∣−4$ | $0$ |

$4$ | $∣4−6∣−4$ | $-2$ |

$6$ | $∣6−6∣−4$ | $-4$ |

$8$ | $∣8−6∣−4$ | $-2$ |

$10$ | $∣10−6∣−4$ | $0$ |

To draw the graph, we will plot and connect the obtained points. Do not forget that the graph of an absolute value function has a V

-shape!

As a result, the graph of the function is given in option **A.**

c

$x$ | $∣x−6∣+4$ | $y$ |
---|---|---|

$0$ | $∣0−6∣+4$ | $10$ |

$2$ | $∣2−6∣+4$ | $8$ |

$4$ | $∣4−6∣+4$ | $6$ |

$6$ | $∣6−6∣+4$ | $4$ |

$8$ | $∣8−6∣+4$ | $6$ |

$10$ | $∣10−6∣+4$ | $8$ |

To draw the graph, we will plot and connect the obtained points. Do not forget that the graph of an absolute value function has a V

-shape!

The graph we have above matches the graph given in option **B.**