Question

use technology to find points and then graph the function $y = 2sqrt3{x + 4} + 4$, 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 pick x-values to simplify the cube root. Let's choose \( x = -4 \), \( x = -3 \), \( x = 0 \), \( x = 4 \).

Step2: Calculate y for \( x = -4 \)

Substitute \( x = -4 \) into \( y = 2\sqrt[3]{x + 4} + 4 \):
\( y = 2\sqrt[3]{-4 + 4} + 4 = 2\sqrt[3]{0} + 4 = 2(0) + 4 = 4 \). So the point is \( (-4, 4) \).

Step3: Calculate y for \( x = -3 \)

Substitute \( x = -3 \):
\( y = 2\sqrt[3]{-3 + 4} + 4 = 2\sqrt[3]{1} + 4 = 2(1) + 4 = 6 \). Point: \( (-3, 6) \).

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

Substitute \( x = 0 \):
\( y = 2\sqrt[3]{0 + 4} + 4 = 2\sqrt[3]{4} + 4 \approx 2(1.587) + 4 \approx 3.174 + 4 = 7.174 \). Point: \( (0, \approx 7.17) \).

Step5: Calculate y for \( x = 4 \)

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

Step6: Calculate y for \( x = -5 \) (optional, but to show another point)

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

Now, plot these points \( (-4, 4) \), \( (-3, 6) \), \( (4, 8) \), \( (-5, 2) \) on the graph.

Answer:

To graph \( y = 2\sqrt[3]{x + 4} + 4 \), plot points like \((-4, 4)\), \((-3, 6)\), \((4, 8)\), and \((-5, 2)\) (or others calculated) on the coordinate plane.