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{{ printedBook.courseTrack.name }} {{ printedBook.name }} We want to graph the given radical function.
$f(x)=x−4 −10 $
To do so, we will start by making a table of values. Recall that the radicand **cannot** be negative. With this in mind, we can first determine its domain as shown below.
$x−4≥0⇔x≥4 $
Therefore, we will use $x-$values *greater than or equal to* $4.$ Let's start!

$x$ | $x−4 −10$ | $f(x)=x−4 −10$ |
---|---|---|

$4$ | $4−4 −10$ | $-10$ |

$5$ | $5−4 −10$ | $-9$ |

$6$ | $6−4 −10$ | $-8.585…$ |

$7$ | $7−4 −10$ | $-8.267…$ |

$8$ | $8−4 −10$ | $-8$ |

$9$ | $9−4 −10$ | $-7.763…$ |

The ordered pairs $(4,-10),$ $(5,-9),$ $(6,-8.585),$ $(7,-8.267),$ $(8,-8),$ and $(9,-7.763)$ all lie on the graph of the function. Now, we will plot and connect these points with a smooth curve.

We can see above that the graph of the function goes to infinity in the positive direction starting from $y=-10.$ Therefore, its range is all real numbers *greater than or equal to* $-10.$
$Domain:Range: x≥4y≥-10 $