Answer:
C. It is a many-to-one function.
Step-by-step explanation:
You want a description of the cubic function f(x) = 2x³ +2x² -x.
Polynomial
Any polynomial relation passes the vertical line test, so is a function (eliminates choices B and D).
Horizontal line test
An even-degree polynomial function will always fail the horizontal line test, so will be a many-to-one function. An odd-degree function will be many-to-one if its slope changes sign.
The slope of the function f(x) is given by its derivative:
f'(x) = 6x² +4x -1
The discriminant of this quadratic will tell us if it changes sign:
d = b² -4ac = 4² -4(6)(-1) = 40
This positive value means the derivative is zero in two places. The graph of the cubic has two (2) turning points.
F(x) is a many-to-one function.
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