Which of the given functions could this graph represent?

a. f(x) = x(x − 1)(x + 1)
b. f(x) = (x − 1)(x − 2)(x + 1)(x + 2)
c. f(x) = x(x − 1)(x − 2)(x + 1)(x + 2)
d. f(x) = x(x − 1)(x − 2)

The answer is B. f(x) = (x − 1)(x − 2)(x + 1)(x + 2)

B. f(x) = (x − 1)(x − 2)(x + 1)(x + 2)

Step-by-step explanation:

Choice A will be a transformation of the function f(x) = x³.  The parent function goes from the third quadrant through the origin into the first quadrant.  This is not a cubic function.

Choice C will be a transformation of the function f(x) = x⁵.  The parent function goes from the third quadrant through the origin into the first quadrant.  This is not one of those functions.

Choice D will be a transformation of the function f(x) = x³.  This is not a cubic function.

Choice D will be a transformation of the function f(x) = x⁴.  These functions go from the second quadrant across the y-axis into the first quadrant.  This is a quartic function.