Question

which graph shows y = 12|x|?

Explanation:

Step1: Analyze the absolute - value function

The function $y = 12|x|$ is an absolute - value function. When $x\geq0$, $y = 12x$; when $x\lt0$, $y=- 12x$. It is a V - shaped graph centered at the origin $(0,0)$.

Step2: Check the slope

The slope of the line for $x\geq0$ is $m = 12$, and the slope of the line for $x\lt0$ is $m=-12$. The graph will be steeper compared to $y = |x|$ because of the coefficient 12.

Answer:

We need to look for a V - shaped graph centered at the origin with a relatively steep slope. Without seeing the exact details of the graphs in a high - resolution way, but based on the general form of $y = 12|x|$, we know it is a symmetric V - shaped graph about the y - axis with a steeper slope than the basic $y = |x|$ graph. If we assume standard scaling on the axes, we can eliminate graphs that are not V - shaped or do not have the correct steepness. However, since the actual visual details of the graphs A, B, C, D are not fully clear from the provided image, we can't precisely pick one among them. But the general characteristics of the graph of $y = 12|x|$ are a V - shaped graph symmetric about the y - axis with a slope of 12 for $x\gt0$ and - 12 for $x\lt0$.