which phrases describe the graph of f(x) = |x|? check all that apply. v - shaped u - shaped opens up opens…

which phrases describe the graph of f(x) = |x|? check all that apply. v - shaped u - shaped opens up opens down symmetric with respect to the x - axis symmetric with respect to the y - axis

which phrases describe the graph of f(x) = |x|? check all that apply. v - shaped u - shaped opens up opens down symmetric with respect to the x - axis symmetric with respect to the y - axis

Answer

Explanation:

Step1: Recall absolute - value function shape

The graph of (y = |x|) is V - shaped.

Step2: Analyze opening direction

For (y = |x|), when (x\geq0), (y = x) and when (x<0), (y=-x). The values of (y) are non - negative, so it opens up.

Step3: Check symmetry

If we replace (x) with (-x) in (y = |x|), we get (y=|-x|=|x|), so the function is symmetric about the y - axis. It is not symmetric about the x - axis because for a point ((x,y)) on (y = |x|), the point ((x, - y)) is not on the graph.

Answer:

A. V - shaped, C. opens up, F. symmetric with respect to the y - axis