Question

If the graph of y = |x| is translated so that the point (1, 1) is moved to (4, 1), what is the equation of the new graph?

y = |x - 3|
y = |x| - 3
y = |x + 3|
y = |x| + 3

Answer 1

we know that

the point
`(1, 1)` is moved to
`(4, 1)`

so

the rule of the translation is

`(x,y)---------> (x+3,y)`

that means

the translation is
`3` units to the right

therefore

the answer is

the equation of the new graph is

`y=\left|x-3\right|`

see the attached figure to better understand the problem

Answer 2

This may be done by plugging in the value of the coordinates of the point (4, 1) in the equation. It may be seen that to get an answer for y of 1, x should be subtracted by 3. We can choice either from first and second choice; however, it is x that is being translated so, -3 should appear inside the absolute value sign.