Question

use technology to find points and then graph the function $y = \sqrt{x + 3}-7$ following the instructions below. plot at least four points with integer coordinates that fit on the axes below. click a point to delete it.

Explanation:

Step1: Choose integer values for x

We need to choose x - values such that \(x + 3\geq0\) (since we have a square - root function) to get real - valued y. Let's start with \(x=-3\).

Step2: Calculate y when \(x = - 3\)

Substitute \(x=-3\) into \(y=\sqrt{x + 3}-7\). Then \(y=\sqrt{-3 + 3}-7=-7\). So the point is \((-3,-7)\).

Step3: Calculate y when \(x=-2\)

Substitute \(x = - 2\) into \(y=\sqrt{x + 3}-7\). Then \(y=\sqrt{-2+3}-7=1 - 7=-6\). So the point is \((-2,-6)\).

Step4: Calculate y when \(x = 1\)

Substitute \(x = 1\) into \(y=\sqrt{x + 3}-7\). Then \(y=\sqrt{1 + 3}-7=2 - 7=-5\). So the point is \((1,-5)\).

Step5: Calculate y when \(x = 6\)

Substitute \(x = 6\) into \(y=\sqrt{x + 3}-7\). Then \(y=\sqrt{6 + 3}-7=3 - 7=-4\). So the point is \((6,-4)\).

Answer:

The points are \((-3,-7),(-2,-6),(1,-5),(6,-4)\)