Question

use technology to find points and then graph the function y = \sqrt3{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

Let's choose \(x = 5\), \(x = 6\), \(x = 13\), \(x=-3\).

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

Substitute \(x = 5\) into \(y=\sqrt[3]{x - 5}-5\). Then \(y=\sqrt[3]{5 - 5}-5=0 - 5=-5\). The point is \((5,-5)\).

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

Substitute \(x = 6\) into \(y=\sqrt[3]{x - 5}-5\). Then \(y=\sqrt[3]{6 - 5}-5=1 - 5=-4\). The point is \((6,-4)\).

Step4: Calculate y - values for \(x = 13\)

Substitute \(x = 13\) into \(y=\sqrt[3]{x - 5}-5\). Then \(y=\sqrt[3]{13 - 5}-5=\sqrt[3]{8}-5=2 - 5=-3\). The point is \((13,-3)\).

Step5: Calculate y - values for \(x=-3\)

Substitute \(x=-3\) into \(y=\sqrt[3]{x - 5}-5\). Then \(y=\sqrt[3]{-3 - 5}-5=\sqrt[3]{-8}-5=-2 - 5=-7\). The point is \((-3,-7)\).

Answer:

The points \((5,-5)\), \((6,-4)\), \((13,-3)\), \((-3,-7)\) can be plotted on the graph.