Question

use technology to find points and then graph the function $y = -2\sqrt3{x + 3} + 3$, following the instructions below.
plot at least four points that fit on the axes below. click a point to delete it.

Explanation:

Step1: Choose x-values

Let's pick x-values to find corresponding y-values. Let's choose x = -3, x = -2, x = 5, x = -11.

Step2: Calculate y for x = -3

Substitute x = -3 into \( y = -2\sqrt[3]{x + 3} + 3 \)
\( y = -2\sqrt[3]{-3 + 3} + 3 = -2\sqrt[3]{0} + 3 = -2(0) + 3 = 3 \)
So the point is (-3, 3)

Step3: Calculate y for x = -2

Substitute x = -2 into the function:
\( y = -2\sqrt[3]{-2 + 3} + 3 = -2\sqrt[3]{1} + 3 = -2(1) + 3 = 1 \)
Point: (-2, 1)

Step4: Calculate y for x = 5

Substitute x = 5:
\( y = -2\sqrt[3]{5 + 3} + 3 = -2\sqrt[3]{8} + 3 = -2(2) + 3 = -4 + 3 = -1 \)
Point: (5, -1)

Step5: Calculate y for x = -11

Substitute x = -11:
\( y = -2\sqrt[3]{-11 + 3} + 3 = -2\sqrt[3]{-8} + 3 = -2(-2) + 3 = 4 + 3 = 7 \)
Point: (-11, 7)

Now we have four points: (-3, 3), (-2, 1), (5, -1), (-11, 7) to plot on the graph.

Answer:

The points to plot are (-3, 3), (-2, 1), (5, -1), (-11, 7) (and then graph the function using these points).