Pergunta

D 2.Choose the function that has the following at approaches positive and negative infinity, f(x) approaches positive infinity. f(x)=-2x^5+2x^4+3 f(x)=x^6+3x^5-x^3 f(x)=2x^5+2x^4+3 f(x)=-x^6+3x^5-x^3
Solução

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VascoElite · Tutor por 8 anos
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To determine which function approaches positive infinity as x approaches positive and negative infinity, we need to analyze the behavior of each function.<br /><br />Let's analyze each function one by one:<br /><br />1. $f(x)=-2x^{5}+2x^{4}+3$<br /> - As x approaches positive infinity, the term $-2x^{5}$ dominates the behavior of the function. Since the coefficient is negative, the function will approach negative infinity.<br /> - As x approaches negative infinity, the term $-2x^{5}$ also dominates the behavior of the function. Since the coefficient is negative, the function will approach positive infinity.<br /><br />2. $f(x)=x^{6}+3x^{5}-x^{3}$<br /> - As x approaches positive infinity, the term $x^{6}$ dominates the behavior of the function. Since the coefficient is positive, the function will approach positive infinity.<br /> - As x approaches negative infinity, the term $x^{6}$ also dominates the behavior of the function. Since the coefficient is positive, the function will approach positive infinity.<br /><br />3. $f(x)=2x^{5}+2x^{4}+3$<br /> - As x approaches positive infinity, the term $2x^{5}$ dominates the behavior of the function. Since the coefficient is positive, the function will approach positive infinity.<br /> - As x approaches negative infinity, the term $2x^{5}$ also dominates the behavior of the function. Since the coefficient is positive, the function will approach negative infinity.<br /><br />4. $f(x)=-x^{6}+3x^{5}-x^{3}$<br /> - As x approaches positive infinity, the term $-x^{6}$ dominates the behavior of the function. Since the coefficient is negative, the function will approach negative infinity.<br /> - As x approaches negative infinity, the term $-x^{6}$ also dominates the behavior of the function. Since the coefficient is negative, the function will approach positive infinity.<br /><br />Based on the analysis, the function that approaches positive infinity as x approaches positive and negative infinity is $f(x)=x^{6}+3x^{5}-x^{3}$.
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