Question

1. $y = |x - 1|$

type of function: absolute value
input x: -2, -1, 0, 1, 2
output $y = |x - 1|$: 3, 2, 1, 0, 1
ordered pair (x, y): (-2, 3), (-1, 2), (0, 1), (1, 0), (2, 1)

Explanation:

Step1: Identify Ordered Pairs

We have the ordered pairs from the table: \((-2, 3)\), \((-1, 2)\), \((0, 1)\), \((1, 0)\), \((2, 1)\).

Step2: Plot Each Point

• For \((-2, 3)\): Move 2 units left on the x - axis and 3 units up on the y - axis.
• For \((-1, 2)\): Move 1 unit left on the x - axis and 2 units up on the y - axis.
• For \((0, 1)\): The point is on the y - axis, 1 unit up.
• For \((1, 0)\): The point is on the x - axis, 1 unit right.
• For \((2, 1)\): Move 2 units right on the x - axis and 1 unit up on the y - axis.

Step3: Connect the Points

Since the function is \(y = |x - 1|\), which is an absolute - value function, the graph should be a V - shaped graph. After plotting the points, we connect them in a way that forms the V - shape of the absolute - value function. The vertex of \(y=|x - h|+k\) is at \((h,k)\), for \(y = |x - 1|\), the vertex is at \((1,0)\), which matches our ordered pair \((1,0)\). When we connect the points, we will see that the left side (for \(x<1\)) has a negative slope and the right side (for \(x > 1\)) has a positive slope, forming the characteristic V - shape of an absolute - value function.

(Note: Since the problem is about graphing the function \(y = |x - 1|\) using the given ordered pairs, the final answer would be the graph plotted with the ordered pairs \((-2,3)\), \((-1,2)\), \((0,1)\), \((1,0)\), \((2,1)\) connected to form the V - shaped graph of the absolute - value function. If we were to describe the graph, it is a V - shaped graph with vertex at \((1,0)\), passing through the other plotted points.)

Answer:

The graph is a V - shaped absolute - value graph with vertex at \((1,0)\), passing through \((-2,3)\), \((-1,2)\), \((0,1)\) and \((2,1)\) (when plotted on the given coordinate grid).