Question

question use technology to find points and then graph the function y = \sqrt{x - 5}-5, following the instructions below. done plotting points plot at least four points that fit on the axes below. click a point to delete it.

Explanation:

Step1: Choose x - values

We need to choose x - values such that \(x−5\geq0\) (since we have a square - root function \(\sqrt{x - 5}\)). Let's choose \(x = 5\), \(x=6\), \(x = 10\), \(x=14\).

Step2: Calculate y - values for \(x = 5\)

Substitute \(x = 5\) into \(y=\sqrt{x - 5}-5\).
\[y=\sqrt{5 - 5}-5=- 5\]
The point is \((5,-5)\).

Step3: Calculate y - values for \(x = 6\)

Substitute \(x = 6\) into \(y=\sqrt{x - 5}-5\).
\[y=\sqrt{6 - 5}-5=1 - 5=-4\]
The point is \((6,-4)\).

Step4: Calculate y - values for \(x = 10\)

Substitute \(x = 10\) into \(y=\sqrt{x - 5}-5\).
\[y=\sqrt{10 - 5}-5=\sqrt{5}-5\approx2.24 - 5=-2.76\]
The point is \((10,\sqrt{5}-5)\approx(10, - 2.76)\).

Step5: Calculate y - values for \(x = 14\)

Substitute \(x = 14\) into \(y=\sqrt{x - 5}-5\).
\[y=\sqrt{14 - 5}-5=\sqrt{9}-5=3 - 5=-2\]
The point is \((14,-2)\).

Answer:

The points \((5,-5)\), \((6,-4)\), \((10,\sqrt{5}-5)\), \((14,-2)\) can be plotted on the graph.