Question

use technology to find points and then graph the function $y = |x - 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.

graph of coordinate plane with x-axis from -10 to 10 and y-axis from -10 to 10

Explanation:

Step1: Identify the full function

The function is $y = |x - 2| - 1$ (the original prompt is missing the constant term, this is the standard form for this type of graph task).

Step2: Choose x-values, solve for y

Pick $x=-1,0,2,4,5$:

• For $x=-1$: $y = |-1 - 2| - 1 = |-3| - 1 = 3 - 1 = 2$ → Point: $(-1,2)$
• For $x=0$: $y = |0 - 2| - 1 = |-2| - 1 = 2 - 1 = 1$ → Point: $(0,1)$
• For $x=2$: $y = |2 - 2| - 1 = |0| - 1 = 0 - 1 = -1$ → Point: $(2,-1)$
• For $x=4$: $y = |4 - 2| - 1 = |2| - 1 = 2 - 1 = 1$ → Point: $(4,1)$
• For $x=5$: $y = |5 - 2| - 1 = |3| - 1 = 3 - 1 = 2$ → Point: $(5,2)$

Step3: Plot points, draw the graph

Plot the 5 points on the axes, then connect them to form a V-shaped graph with vertex at $(2,-1)$.

Answer:

Points to plot: $(-1, 2)$, $(0, 1)$, $(2, -1)$, $(4, 1)$, $(5, 2)$
The graph is a V-shaped absolute value function with vertex at $(2, -1)$, opening upwards.