Question

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

done plotting points
plot at least five points that fit on the axes below. click a point to delete it.
(graph with x and y axes, grid, and axes labels from -10 to 10)

Explanation:

Step1: Choose x-values

Select x - values like \(x=-7, x = 0, x = 1, x = 2, x = 9\) (these are easy to compute cube roots for).

Step2: Calculate y for \(x=-7\)

Substitute \(x=-7\) into \(y=\sqrt[3]{x}-1\). We know that \(\sqrt[3]{-7}\approx - 1.913\), so \(y=\sqrt[3]{-7}-1\approx-1.913 - 1=-2.913\). So the point is \((-7,-2.913)\).

Step3: Calculate y for \(x = 0\)

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

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

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

Step5: Calculate y for \(x = 2\)

Substitute \(x = 2\) into the function: \(\sqrt[3]{2}\approx1.26\), so \(y=\sqrt[3]{2}-1\approx1.26 - 1 = 0.26\). The point is \((2,0.26)\).

Step6: Calculate y for \(x = 9\)

Substitute \(x = 9\) into the function: \(\sqrt[3]{9}\approx2.08\), so \(y=\sqrt[3]{9}-1\approx2.08 - 1=1.08\). The point is \((9,1.08)\).

(To graph, plot these points \((-7,-2.913)\), \((0,-1)\), \((1,0)\), \((2,0.26)\), \((9,1.08)\) on the coordinate plane and draw a smooth curve through them as the cube - root function is continuous.)

Answer:

To graph \(y = \sqrt[3]{x}-1\), plot points such as \((-7,-2.913)\), \((0,-1)\), \((1,0)\), \((2,0.26)\), \((9,1.08)\) (and draw a smooth curve through them).