For the polynomial

MATHEMATICS · Single correct · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

For the polynomial p(x)=−2x6+5x4−1p(x)=-2x^{6}+5x^{4}-1, what happens to p(x)p(x) as xx approaches +∞+\infty and −∞-\infty? (a) p(x)→+∞p(x)\to+\infty as x→±∞x\to\pm\infty (b) p(x)→−∞p(x)\to-\infty as x→+∞x\to+\infty and p(x)→−∞p(x)\to-\infty as x→−∞x\to-\infty (c) p(x)→−∞p(x)\to-\infty as x→+∞x\to+\infty and p(x)→+∞p(x)\to+\infty as x→−∞x\to-\infty (d) p(x)→+∞p(x)\to+\infty as x→+∞x\to+\infty and p(x)→−∞p(x)\to-\infty as x→−∞x\to-\infty

Related theory

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