Pergunta

33. Predict the end behavior of f(x)=-(1)/(4)x^4-2x^2+8 As zz approaches negative infinity, f(x) approaches positive infinity. As approaches positive infinity, f(x) approaches negative infinity. As zrapproaches positive and negative infinity, f(x) approaches negative infinity. As z approaches positive and negative infinity, f(x) approaches positive infinity. As z approaches negative infinity, f(x) approaches negative infinity.As at approaches positive infinity. f(x) approaches positive infinity.
Solução

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ValdomiroProfissional · Tutor por 6 anos
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To predict the end behavior of the polynomial function $f(x)=-\frac{1}{4}x^{4}-2x^{2}+8$, we need to consider the leading term, which is the term with the highest power of $x$. In this case, the leading term is $-\frac{1}{4}x^{4}$.<br /><br />Since the coefficient of the leading term is negative, the graph of the function will fall to the left and right as $x$ approaches positive and negative infinity. Therefore, the correct answer is:<br /><br />As $x$ approaches positive and negative infinity, $f(x)$ approaches negative infinity.
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