Question

Use the tables to answer the question.

This table shows the x-values and Corresponding f(x) Values.
x f(x)
−2
2
−1
1
0 0
1 1
2 2
3 3
This table shows the x-values and Corresponding f(x ± k) Values.
x f(x±k)
−2
4
−1
3
0 2
1 1
2 0
3 1
The first table represents the function y=|x|
, and the second table represents the horizontal translation of the original function. Which of the following statements is true about the parent function and its translation?

(1 point)
Responses

The parent function was shifted 2 units to the right, resulting in the translated function y=|x−2|
.
The parent function was shifted 2 units to the right, resulting in the translated function y equals Start Absolute Value x minus 2 End Absolute Value .

The parent function was shifted 2 units up, resulting in the translated function y=|x−2|
.
The parent function was shifted 2 units up, resulting in the translated function y equals Start Absolute Value x minus 2 End Absolute Value .

The parent function was shifted 2 units to the right, resulting in the translated function y=|x+2|
.
The parent function was shifted 2 units to the right, resulting in the translated function y equals Start Absolute Value x plus 2 End Absolute Value .

The parent function was shifted 2 units to the left, resulting in the translated function y=|x+2|
.

Answer 1

The parent function was shifted 2 units to the right, resulting in the translated function y = |x − 2|.

Reason: the vertex (0,0) of y = |x| moves to (2,0) and values match |x−2| (e.g. f(2)=0, f(3)=1, f(0)=2).