Consider the polynomial functionh(x)=x6−3x5−17x3. What is the end behavior of the graph of h ?Choose 1 answer:(A) As x→∞,h(x)→∞, and as x→−∞, h(x)→∞.(B) As x→∞, h(x)→−∞, and as x→−∞,h(x)→∞.(C) As x→∞, h(x)→−∞, and as x→−∞,h(x)→−∞.(D) As x→∞,h(x)→∞, and as x→−∞, h(x)→−∞.
Q. Consider the polynomial functionh(x)=x6−3x5−17x3. What is the end behavior of the graph of h ?Choose 1 answer:(A) As x→∞,h(x)→∞, and as x→−∞, h(x)→∞.(B) As x→∞, h(x)→−∞, and as x→−∞,h(x)→∞.(C) As x→∞, h(x)→−∞, and as x→−∞,h(x)→−∞.(D) As x→∞,h(x)→∞, and as x→−∞, h(x)→−∞.
Identify Leading Term: Identify the leading term of the polynomial function. The leading term of the polynomial function h(x)=x6−3x5−17x3 is x6, since it has the highest power of x.
Determine End Behavior: Determine the end behavior based on the leading term.The end behavior of a polynomial function is determined by its leading term. Since the leading term is x6, which is an even power, the end behavior will be the same in both directions of the x-axis. As x approaches positive infinity (x→∞), x6 will also approach positive infinity. Similarly, as x approaches negative infinity (x→−∞), x6 will also approach positive infinity because an even power of a negative number is positive.
Choose Correct Answer: Choose the correct answer based on the end behavior.Based on the end behavior determined in Step 2, the correct answer is:(A) As x→∞, h(x)→∞, and as x→−∞, h(x)→∞.
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