Question

Question 7 of 10

Which statement best describes the function below?
f(x) = 2x³+2x²-x
A. It is a one-to-one function.
B. It fails the vertical line test.
C. It is a many-to-one function.
D. It is not a function.
SUBMIT

Answer 1

C. It is a many-to-one function.

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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