Question

question
use technology to find points and then graph the function $y = -2\sqrt3{x} - 1$, following the instructions below.

done plotting points
plot at least five points that fit on the axes below. click a point to delete it.

Explanation:

Step1: Choose x-values

Select x - values such as \(x=-8, -1, 0, 1, 8\) (these are perfect cubes or simple values to make the cube - root calculation easy).

Step2: Calculate y for \(x = - 8\)

Substitute \(x=-8\) into the function \(y=-2\sqrt[3]{x}-1\). We know that \(\sqrt[3]{-8}=-2\), so \(y=-2\times(-2)-1 = 4 - 1=3\). So the point is \((-8,3)\).

Step3: Calculate y for \(x=-1\)

Substitute \(x = - 1\) into the function. Since \(\sqrt[3]{-1}=-1\), then \(y=-2\times(-1)-1=2 - 1 = 1\). The point is \((-1,1)\).

Step4: Calculate y for \(x = 0\)

Substitute \(x = 0\) into the function. \(\sqrt[3]{0}=0\), so \(y=-2\times0-1=-1\). The point is \((0, - 1)\).

Step5: Calculate y for \(x = 1\)

Substitute \(x = 1\) into the function. \(\sqrt[3]{1}=1\), so \(y=-2\times1-1=-2 - 1=-3\). The point is \((1,-3)\).

Step6: Calculate y for \(x = 8\)

Substitute \(x = 8\) into the function. \(\sqrt[3]{8}=2\), so \(y=-2\times2-1=-4 - 1=-5\). The point is \((8,-5)\).

After calculating these points \((-8,3)\), \((-1,1)\), \((0, - 1)\), \((1,-3)\), \((8,-5)\), you can plot them on the coordinate plane and then draw the curve of the function \(y=-2\sqrt[3]{x}-1\) through these points.

Answer:

The points to plot are \((-8,3)\), \((-1,1)\), \((0, - 1)\), \((1,-3)\), \((8,-5)\). After plotting these points, draw the curve of the function \(y = - 2\sqrt[3]{x}-1\) through them.