Consider the polynomial functionp(x)=−5x6−3x5+4x2+6x. What is the end behavior of the graph of p ?Choose 1 answer:(A) As x→∞,p(x)→∞, and as x→−∞, p(x)→∞.(B) As x→∞, p(x)→−∞, and as x→−∞,p(x)→∞.(C) As x→∞, p(x)→−∞, and as x→−∞,p(x)→−∞.(D) As x→∞,p(x)→∞, and as x→−∞, p(x)→−∞.
Q. Consider the polynomial functionp(x)=−5x6−3x5+4x2+6x. What is the end behavior of the graph of p ?Choose 1 answer:(A) As x→∞,p(x)→∞, and as x→−∞, p(x)→∞.(B) As x→∞, p(x)→−∞, and as x→−∞,p(x)→∞.(C) As x→∞, p(x)→−∞, and as x→−∞,p(x)→−∞.(D) As x→∞,p(x)→∞, and as x→−∞, p(x)→−∞.
Leading Term Exponent: Since the leading term has an even exponent, the end behaviors at both ends of the x-axis will be the same.
Coefficient Sign: Because the coefficient of the leading term is negative, the graph will go down on both ends.
End Behavior: So, as x approaches ∞, p(x) approaches −∞, and as x approaches −∞, p(x) also approaches −∞.