QuestionDetermine the end behavior of $y$ as $x \to -\infty$ for the equation $y=-4x^{5}+4x^{2}-8$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is $y=-4 x^{5}+4 x^{}-8$ . We are interested in the end behavior of $y$ as $x$ approaches negative infinity

STEP 2

In order to determine the end behavior of a function, we need to look at the highest degree term in the equation. This is because as $x$ goes to positive or negative infinity, the highest degree term will dominate the behavior of the function.
In our case, the highest degree term is $-4x^5$ .

STEP 3

Since the highest degree term is $-x^5$ , the end behavior of the function will be determined by this term.The coefficient of this term is negative and the degree is odd.

STEP 4

When the degree of the highest degree term is odd and the coefficient is negative, as $x$ goes to negative infinity, $y$ goes to positive infinity.
So, the end behavior of $y$ as $x$ goes to negative infinity in the equation $y=-4 x^{}+4 x^{2}-8$ is that $y$ goes to positive infinity.

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