Question

use technology to find points and then graph the function $y = 2|x - 4| - 2$, following the instructions below.
done plotting points
plot at least five points that fit on the axes below. click a point to delete it.

Explanation:

Step1: Choose x-values

Let's pick x - values: 2, 3, 4, 5, 6.

Step2: Calculate y for x = 2

Substitute x = 2 into \(y = 2|x - 4|-2\).
\(y=2|2 - 4|-2=2|-2|-2 = 2\times2-2=4 - 2 = 2\). So the point is (2, 2).

Step3: Calculate y for x = 3

Substitute x = 3 into \(y = 2|x - 4|-2\).
\(y=2|3 - 4|-2=2|-1|-2=2\times1 - 2=2 - 2 = 0\). So the point is (3, 0).

Step4: Calculate y for x = 4

Substitute x = 4 into \(y = 2|x - 4|-2\).
\(y=2|4 - 4|-2=2|0|-2=0 - 2=-2\). So the point is (4, - 2).

Step5: Calculate y for x = 5

Substitute x = 5 into \(y = 2|x - 4|-2\).
\(y=2|5 - 4|-2=2|1|-2=2\times1 - 2=0\). So the point is (5, 0).

Step6: Calculate y for x = 6

Substitute x = 6 into \(y = 2|x - 4|-2\).
\(y=2|6 - 4|-2=2|2|-2=4 - 2 = 2\). So the point is (6, 2).

To graph the function, plot the points (2, 2), (3, 0), (4, - 2), (5, 0), (6, 2) and draw a V - shaped graph (since it's an absolute value function) passing through these points. The vertex of the absolute value function \(y=a|x - h|+k\) is at (h, k), here h = 4, k=-2, so the vertex is (4, - 2). The slope of the right - hand side (when x>4) is 2 and the slope of the left - hand side (when x < 4) is - 2.

Answer:

The points to plot are (2, 2), (3, 0), (4, - 2), (5, 0), (6, 2) (and the graph is a V - shaped graph with vertex at (4, - 2), opening upwards with a vertical stretch factor of 2).