We need to circle each function with the same range of y = | x |
So, let check the options:
Before i start, let me give you some tips:
if the function shifted right or left the range will not changed
if the function shifted up or down the range will be changed
Let is continue the answer
So,
y = | x - 2 |
As the function shifted to the right 2 units,
the range will not changed
See the following image as a prove
y = - | x - 2 |
This function is the minus of | x - 2 |
So, the range will be changed
y = | x + 7|
The function is shifted 7 units to the left
The range will not be changed
y = |x | - 7
The function is shifted 7 units down
So, the range will be changed
As a summery
The function that will have the same range as y = | x |
Are:
y = | x - 2 | and y = | x + 7 |