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

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

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DelcieRiveria DelcieRiveria · Answer 2 · 2019-05-07T06:22:03+02:00

Answer:

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

Step-by-step explanation:

The given function are

[tex]f(x)=|x|[/tex]

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

[tex]g(x)=|x|-4[/tex] ..... (1)

The translation of the function is defined as

[tex]g(x)=|x+a|+b[/tex] .... (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

[tex]a=0,b=-4[/tex]

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