Which of the following best describes the end behavior of the function f(x) = -x

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Question: Which of the following best describes the end behavior of the function f(x) = -x^4?

Options:

Both ends go to positive infinity.
Both ends go to negative infinity.
The left end goes to negative infinity and the right end goes to positive infinity.
The left end goes to positive infinity and the right end goes to negative infinity.

Correct Answer: Both ends go to negative infinity.

Solution:

Since the leading coefficient is negative and the degree is even, both ends of the graph will go to negative infinity.

Which of the following best describes the end behavior of the function f(x) = -x^4?

Both ends go to positive infinity.
Both ends go to negative infinity.
The left end goes to negative infinity and the right end goes to positive infinity.
The left end goes to positive infinity and the right end goes to negative infinity.

Which of the following best describes the end behavior of the function f(x) = -x^4?

Step 1: Identify the function given, which is f(x) = -x^4.
Step 2: Determine the degree of the polynomial. The degree is 4, which is even.
Step 3: Look at the leading coefficient, which is -1 (the coefficient of x^4). Since it is negative, it will affect the end behavior.
Step 4: For even degree polynomials, if the leading coefficient is negative, both ends of the graph will go down.
Step 5: Conclude that as x approaches positive infinity (x → ∞), f(x) approaches negative infinity (f(x) → -∞).
Step 6: Also conclude that as x approaches negative infinity (x → -∞), f(x) also approaches negative infinity (f(x) → -∞).
Step 7: Therefore, the end behavior of the function f(x) = -x^4 is that both ends go to negative infinity.

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