which graph represents the function f(x) = |x| - 4?

Explanation:

Step1: Recall properties of absolute - value function

The parent absolute - value function is $y = |x|$, which has a vertex at $(0,0)$ and opens upwards. The general form of a vertical translation of a function $y = f(x)$ is $y=f(x)+k$, where $k$ is a constant.

Step2: Analyze the given function

For the function $f(x)=|x|-4$, it is a vertical translation of the parent function $y = |x|$ by $k=-4$ units.

Step3: Determine the vertex

The vertex of the function $y = |x|$ is $(0,0)$. After a vertical translation of 4 units down (since $k = - 4$), the vertex of the function $f(x)=|x|-4$ is $(0, - 4)$.

Answer:

The graph of the function $f(x)=|x|-4$ is a V - shaped graph with the vertex at the point $(0,-4)$ and opening upwards.