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. Let's take x = 5, x = 6, x = 4, x = 13.

Step2: Calculate y for x = 5

Substitute x = 5 into \( y = 2\sqrt[3]{x - 5} \). Then \( x - 5 = 0 \), so \( y = 2\sqrt[3]{0}=0 \). So point (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 = 4

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

Step5: Calculate y for x = 13

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

(To graph, plot these points: (4, -2), (5, 0), (6, 2), (13, 4) and draw the curve through them.)

Answer:

Points to plot: (4, -2), (5, 0), (6, 2), (13, 4) (and graph the cube - root function transformed by vertical stretch and horizontal shift)