Question

use technology to find points and then graph the function $y = 2|x - 1| + 4$, following the instructions below.

done plotting points

plot at least five points that fit on the axes below. click a point to delete it.

graph with x-axis from -10 to 10 and y-axis from -10 to 10

Explanation:

Step1: Choose x-values

Let's pick x-values: -1, 0, 1, 2, 3.

Step2: Calculate y for x=-1

Substitute x=-1 into \( y = 2|x - 1| + 4 \):
\( y = 2|-1 - 1| + 4 = 2| -2 | + 4 = 2(2) + 4 = 8 \).
Point: (-1, 8)

Step3: Calculate y for x=0

Substitute x=0:
\( y = 2|0 - 1| + 4 = 2| -1 | + 4 = 2(1) + 4 = 6 \).
Point: (0, 6)

Step4: Calculate y for x=1

Substitute x=1:
\( y = 2|1 - 1| + 4 = 2|0| + 4 = 0 + 4 = 4 \).
Point: (1, 4)

Step5: Calculate y for x=2

Substitute x=2:
\( y = 2|2 - 1| + 4 = 2|1| + 4 = 2 + 4 = 6 \).
Point: (2, 6)

Step6: Calculate y for x=3

Substitute x=3:
\( y = 2|3 - 1| + 4 = 2|2| + 4 = 4 + 4 = 8 \).
Point: (3, 8)

Answer:

Five points are (-1, 8), (0, 6), (1, 4), (2, 6), (3, 8). These can be plotted on the graph.