Determine the end behavior of the polynomial $$ y=-x^{5}+3 x^{2}-x+4 $$ The leading term is $$ \square $$ (write it as one term and use $$ \wedge $$ for exponent, for example: $$ -3 x^{\wedge} 8 $$ ) The leading coefficient is between positive and negative and write that word. Do NOT write a number.) The degree is Therefore, as $$ x \rightarrow \infty $$, then $$ y \rightarrow \square $$ (choose between even and odd and write that word. Do NOT write a number.) inf, and for negative infinity, write -inf).

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To determine the end behavior of the polynomial $$ y=-x^{5}+3x^{2}-x+4 $$, we need to identify the leading term, the leading coefficient, and the degree of the polynomial.

1. Leading Term:
The leading term of a polynomial is the term with the highest degree. In this case, the term with the highest degree is $$ -x^{5} $$. Therefore, the leading term is $$ -x^{5} $$.

2. Leading Coefficient:
The leading coefficient is the coefficient of the leading term. In this case, the leading coefficient is -1.

3. Degree:
The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the degree of the polynomial is 5.

Now, let's determine the end behavior of the polynomial as $$ x \rightarrow \infty $$ and as $$ x \rightarrow -\infty $$.

As $$ x \rightarrow \infty $$, the term with the highest degree, $$ -x^{5} $$, will dominate the behavior of the polynomial. Since the leading coefficient is negative, the polynomial will approach negative infinity as $$ x \rightarrow \infty $$.

As $$ x \rightarrow -\infty $$, the term with the highest degree, $$ -x^{5} $$, will still dominate the behavior of the polynomial. Since the leading coefficient is negative, the polynomial will approach positive infinity as $$ x \rightarrow -\infty $$.

Therefore, as $$ x \rightarrow \infty $$, $$ y \rightarrow -\infty $$, and as $$ x \rightarrow -\infty $$, $$ y \rightarrow \infty $$.
The leading term is $$ -x^{5} $$, the leading coefficient is negative, and the degree is 5. As $$ x \rightarrow \infty $$, $$ y \rightarrow -\infty $$, and as $$ x \rightarrow -\infty $$, $$ y \rightarrow \infty $$.

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