Which statement correctly describes the end behavior of f(x) = -9x^4 + 3x^3 + 3x^2 - 1?
As x goes to infinity, f(x) goes to infinity, and as x goes to negative infinity, f(x) goes to infinity.
As x goes to infinity, f(x) goes to negative infinity, and as x goes to negative infinity, f(x) goes to infinity.
As x goes to infinity, f(x) goes to infinity, and as x goes to negative infinity, f(x) goes to negative infinity.
As x goes to infinity, f(x) goes to negative infinity, and as x goes to negative infinity, f(x) goes to negative infinity.
As x goes to infinity, f(x) goes to negative infinity, and as x goes to negative infinity, f(x) goes to negative infinity.
To the 4th power is "w" shaped. Then, because it is a negative coefficient, it is going to negative infinity so it is an upside down "w".
To determine the end behavior of a function, we look at the leading term of the function. The leading term is the term with the highest exponent. In this case, the leading term is -9x^4.
When the leading term has an even exponent and a negative coefficient, as in -9x^4, this means that as x approaches infinity (positive infinity), the function will also approach negative infinity. Therefore, the correct statement is:
As x goes to infinity, f(x) goes to negative infinity.
Similarly, when x approaches negative infinity, the function will also approach negative infinity. So, the correct statement also includes:
As x goes to negative infinity, f(x) goes to negative infinity.
Therefore, the correct answer is:
As x goes to infinity, f(x) goes to negative infinity, and as x goes to negative infinity, f(x) goes to negative infinity.