Question

If f(x) = |x| and g(x) = |x| − 4, which translation is applied to f(x) to get g(x)?

Answer 1

A vertical translation of 4 units down

Explanation:

The "-4" doesn't affect the x variable, it just reduces the overall 'y' value by 4 units. It brings the y value down by 4 units, so there is a vertical shift of 4 units down

Answer 2

The graph of f(x) translate 4 units down.

Explanation:

The given function are

`f(x)=|x|`

The vertex of this function is (0,0).

`g(x)=|x|-4` ..... (1)

The translation of the function is defined as

`g(x)=|x+a|+b` .... (2)

Where a is horizontal shift and b is vertical shift.

If a<0, then graph shifts a units right and if a>0, then graph shifts a units left.

If b<0, then graph shifts b units down and if a>0, then graph shifts b units up.

From (1) and (2), we get

`a=0,b=-4`

Since b=-4<0, therefore the graph of f(x) shifts 4 units down.