Question

use technology to find points and then graph the function $y = 2sqrt3{x - 5}$, 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 pick x-values to find corresponding y-values. Let's choose x = 5, x = 6, x = 13, x = -3 (these are easy to compute the cube root for).

Step2: Calculate y for x = 5

Substitute x = 5 into \( y = 2\sqrt[3]{x - 5} \). Then \( x - 5 = 0 \), so \( \sqrt[3]{0}=0 \), and \( y = 2\times0 = 0 \). So the point is (5, 0).

Step3: Calculate y for x = 6

Substitute x = 6: \( x - 5 = 1 \), \( \sqrt[3]{1}=1 \), so \( y = 2\times1 = 2 \). Point: (6, 2).

Step4: Calculate y for x = 13

Substitute x = 13: \( x - 5 = 8 \), \( \sqrt[3]{8}=2 \), so \( y = 2\times2 = 4 \). Point: (13, 4).

Step5: Calculate y for x = -3

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

Answer:

The four points are (5, 0), (6, 2), (13, 4), (-3, -4). You can plot these points on the graph.