Write an equation that represents a vertical translation 7 units down of the graph g (x) = |x|

f (x) = |x| - 7

Step-by-step explanation:

The given equation is g (x) = |x| ... (1)

The vertical translation by 7 units down will not change the value of x, the only change will be in the value of g (x).

The vertical translation by 7 units down will change the value of g (x) by [g (x) + 7] in the left-hand side of the equation (1).

Therefore, the equation will become g (x) + 7 = |x|

⇒ g (x) = |x| - 7.

Otherwise we can represent the function as some other name say f (x).

So, f (x) = |x| - 7. (Answer)