Which of the following correctly describes the end behavior of the polynomial function f(x)=-x^3+x^2-4x+2

The left end goes up and the right end goes down.

Step-by-step explanation:

Lets solve the function first and then find out the end behavior of the polynomial:

The given function is  f(x)=-x^3+x^2-4x+2

First step is: Identify the degree of the polynomial. For this we have to  find out the variable with the largest exponent.

The variable with the largest exponent in the given function is -x³

The degree of the polynomial is the largest exponent on the variable.

3 is the degree of the polynomial.

Since the degree is Odd, the ends of the function will point in the opposite direction.

Now find out the leading coefficient of the polynomial which is -1.

Since the leading coefficient is negative the graph falls to the right.

To find the behavior we have to use the degree of the polynomial as well as the sign of leading coefficient.

If it is ODD and NEGATIVE then the the left end goes up and the right end goes down.

Therefore the end behavior of the given function will be described as "the the left end goes up and the right end goes down"

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