Question

Which of the following equations is the translation 2 units down of the graph of y = |x |?

y = |x - 2|
y = |x + 2|
y = |x | - 2
y = |x | + 2

Answer 1

y=|x|-2

this can be easily seen by testing f(0) for all functions:
f1(0)=|0-2|=2
f2(0)=|x+2|=2
f3(0)=|x|-2=-2
f4(0)=|x|+2=2

f(0)=|x|=0, because you want to translate it 2 units down -2 is the expected value

Answer 2

`y=|x|-2`

Explanation:

Given :
`y = |x|`

To Find: Which of the following equations is the translation 2 units down of the graph of
`y = |x|`?

Solution:

Rule : f(x)→f(x)-b

The graph f(x) is translated down by b units

We are given the graph of
`y = |x|`

Now we are supposed to find which equation is the translation 2 units down of the graph of y = |x |?

Using Rule :
`y=|x|=|x|-2`

So, The equation of translated graph is
`y=|x|-2`

So, Option C is correct.