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

Explanation:

Step1: Analyze absolute - value function

The general form of an absolute - value function is $y = a|x|$. When $x\geq0$, $f(x)=4x$; when $x < 0$, $f(x)=-4x$.

Step2: Check key points

When $x = 0$, $f(0)=4\times|0| = 0$. When $x = 1$, $f(1)=4\times|1| = 4$. When $x=-1$, $f(-1)=4\times|-1| = 4$.

Step3: Identify the graph

The graph of $y = 4|x|$ is a V - shaped graph with the vertex at the origin $(0,0)$ and is steeper than the graph of $y = |x|$ because of the coefficient 4.

Answer:

The graph with a V - shape, vertex at the origin $(0,0)$ and passing through the points $(1,4)$ and $(-1,4)$. (Since no specific graph is labeled, you would choose the graph that matches these characteristics among the given options).