Question

Compare the end behavior of the two functions.

f(x)=−2x3g(x)=5x4
Multiple choice question.
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A)
The end behavior is the same as x→−∞ and the same as x→∞.
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B)
The end behavior is the same as x→−∞ and opposite as x→∞.
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C)
The end behavior is opposite as x→−∞ and the same as x→∞.
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D)
The end behavior is opposite as x→−∞ and opposite as x→∞.

Answer 1

Explanation:

To determine the end behavior of the functions f(x) and g(x), we need to look at the highest power terms in each function and their coefficients.

For f(x) = -2x^3, the highest power term is x^3, and the coefficient is -2. As x approaches positive or negative infinity, the value of -2x^3 becomes very large in magnitude and negative. Therefore, the end behavior of f(x) as x approaches infinity or negative infinity is that f(x) → -∞.

For g(x) = 5x^4, the highest power term is x^4, and the coefficient is 5. As x approaches positive or negative infinity, the value of 5x^4 becomes very large in magnitude and positive. Therefore, the end behavior of g(x) as x approaches infinity or negative infinity is that g(x) → ∞.

Since the end behavior of f(x) and g(x) is opposite as x approaches infinity or negative infinity, the correct answer is (D) The end behavior is opposite as x→−∞ and opposite as x→∞.