The graph of which function has the same end benavior as the graph of \( f(x)=-x^{2} \) ? \[ \begin{array}{l}h(x)=(x)=x^{4} \\ h(x)=-x^{5} \\ k(x)--x^{5}\end{array} \]

The function \( f(x) = -x^{2} \) is a downward-opening parabola, meaning it goes to positive infinity as \( x \) approaches negative infinity and to positive infinity as \( x \) approaches positive infinity. Functions with the same end behavior will also need to exhibit this same characteristic. Both \( h(x) = x^{4} \) and \( h(x) = -x^{5} \) will not have the same end behavior as \( f(x) = -x^{2} \); they diverge from the desired characteristics. However, function \( k(x) = -x^{5} \) does show downward movement as \( x \) increases, matching that of our quadratic. Thus, \( k(x) \) has the same end behavior as \( f(x) \).