Question

Which statement best describes the function below?

f(x) = 2x^3 + 2x^2-x
) A. It is a many-to-one function.
B. It is a one-to-one function.
C. It is not a function.
D. It fails the vertical line test.​

Answer 1

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

Explanation:

Hello! It will be a pleasure to help to figure out what's the correct answer to this problem. First of all, we have the following function:

`f(x) = 2x^3 + 2x^2-x`

When plotting this function, we get the red graph of the function shown below. So let's solve this as follows:

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

True

A function is said to be many-to-one there are values of the dependent variable (y-values) that corresponds to more than one value of the independent variable (x-values). To test this, we need to use the Horizontal Line Test. So let's take the horizontal line
`y=0.5`, and you can see from the first figure below that
`y=0.5` is mapped onto
`x=-1.241 \ x=-0.344 \ and \ x=0.585`. so this is a many-to-one function.

B. It is a one-to-one function.

False

Since this is a many-to-one function, it can't be a one-to-one function.

C. It is not a function.

False

Indeed, this is a function

D. It fails the vertical line test.​

False

It passes the vertical line test because any vertical line can intersect the graph of the function at most once. An example of this is shown in the second figure below.