Question

Which function represents the graph of f(x)=−4|x| after it is translated 3 units down?

Answer 1

The function with blue line (see attachment) represents the graph of
`f(x) = -4\cdot |x|` after it is translated 3 units down.

Explanation:

Mathematically speaking, a translation in the y-direction is defined by the following expression:

`g(x) = f(x) + k` (1)

Where:

`g(x)` - Resulting function.

`f(x)` - Original function.

`k` - Translation factor (
`k > 0` - Translation in the +y direction/
`k< 0` - Translation in the -y direction).

If we know that original function is translated 3 units down and
`f(x) = -4\cdot |x|`, then the resulting function is:

`g(x) = -4\cdot |x|-3`

Lastly, we graph both original and resulting functions with the help of a graphing tool, whose outcome is presented in the image attached below:

Please notice that the red line represents the original function, whereas the blue line represents the resulting function.