The question says and asks for the graph of y = p(x)—meaning the graph of
.
The smallest that y can be is , because the absolute value of anything is nonnegative. That narrows
the choices to (A) and (C). Notice that (D) and (E) cannot be functions, because for some values of x
they show two associated values of y. A function, by definition, yields no more than one y for any
particular x.
To choose between (A) and (C), think about what value of x yields .
So the graph reaches its minimum point at x = 2, which means the answer must be (A).