Use the Leading Coefficient Test to determine the end behavior of the polynomial function.
f(x)=-3x^3-3x^2-2x+1
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For n odd:
1.If the leading coefficient is positive, the graph falls to the left and rises to the right.
2.If the leading coefficient is negative, the graph rises to the left and falls to the right.
For n even:
1.If the leading coefficient is positive, the graph rises to the left and to the right.
2.If the leading coefficient is negative, the graph falls to the left and to the right.
In this case, n=2, is even. Here the leading coefficent -3 is negative.
How did you get n?
n is the order of the equation. as in x to the second power.
To determine the end behavior of the polynomial function, you can use the Leading Coefficient Test.
The Leading Coefficient Test states that the end behavior of a polynomial function is determined by the sign of the coefficient of the term with the highest degree.
In this case, the polynomial function is f(x) = -3x^3 - 3x^2 - 2x + 1. The term with the highest degree is -3x^3, and the coefficient is -3.
Since the coefficient is negative (-3), the end behavior of the function is as follows:
- As x approaches negative infinity, the function values will tend to negative infinity.
- As x approaches positive infinity, the function values will tend to positive infinity.
Therefore, the end behavior of the given polynomial function is as x approaches negative infinity, f(x) approaches negative infinity, and as x approaches positive infinity, f(x) approaches positive infinity.