Question

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

Answer 1

Answer:

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

Step-by-step 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.