To determine the end behavior of the function \( f(x) = -8x^4 - 2x^3 + x \), we focus primarily on the leading term, which is \( -8x^4 \).
The leading term of a polynomial function dominates the end behavior as \( x \) approaches positive or negative infinity.
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As \( x \to -\infty \):
- The leading term \( -8x^4 \) tends to \( -\infty \) because raising a negative number to an even power (4) gives a positive number, and multiplying by -8 makes it negative.
- Therefore, \( f(x) \to -\infty \).
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As \( x \to \infty \):
- The leading term \( -8x^4 \) tends to \( -\infty \).
- Thus, \( f(x) \to -\infty \).
Putting it all together, the end behavior of the graph can be described as:
- \( f(x) \to -\infty \) as \( x \to -\infty \)
- \( f(x) \to -\infty \) as \( x \to \infty \)
Therefore, the correct response is: f(x) right arrow negative infinity as x right arrow negative infinity and f(x) right arrow negative infinity as x right arrow infinity.
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