Asked by lol
Which describes the end behavior of the graph of the function f left parenthesis x right parenthesis equals negative 8 x superscript 4 baseline minus 2 x cubed plus x?
(1 point)
Responses
f left parenthesis x right parenthesis right arrow infinity as x right arrow negative infinity and f left parenthesis x right parenthesis right arrow infinity as x right arrow infinity
Image with alt text: f left parenthesis x right parenthesis right arrow infinity as Image with alt text: x right arrow negative infinity and Image with alt text: f left parenthesis x right parenthesis right arrow infinity as Image with alt text: x right arrow infinity
f left parenthesis x right parenthesis right arrow negative infinity as x right arrow negative infinity and f left parenthesis x right parenthesis right arrow negative infinity as x right arrow infinity
Image with alt text: f left parenthesis x right parenthesis right arrow negative infinity as Image with alt text: x right arrow negative infinity and Image with alt text: f left parenthesis x right parenthesis right arrow negative infinity as Image with alt text: x right arrow infinity
f left parenthesis x right parenthesis right arrow infinity as x right arrow negative infinity and f left parenthesis x right parenthesis right arrow negative infinity as x right arrow infinity
Image with alt text: f left parenthesis x right parenthesis right arrow infinity as Image with alt text: x right arrow negative infinity and Image with alt text: f left parenthesis x right parenthesis right arrow negative infinity as Image with alt text: x right arrow infinity
f left parenthesis x right parenthesis right arrow negative infinity as x right arrow negative infinity and f left parenthesis x right parenthesis right arrow infinity as x right arrow infinity
(1 point)
Responses
f left parenthesis x right parenthesis right arrow infinity as x right arrow negative infinity and f left parenthesis x right parenthesis right arrow infinity as x right arrow infinity
Image with alt text: f left parenthesis x right parenthesis right arrow infinity as Image with alt text: x right arrow negative infinity and Image with alt text: f left parenthesis x right parenthesis right arrow infinity as Image with alt text: x right arrow infinity
f left parenthesis x right parenthesis right arrow negative infinity as x right arrow negative infinity and f left parenthesis x right parenthesis right arrow negative infinity as x right arrow infinity
Image with alt text: f left parenthesis x right parenthesis right arrow negative infinity as Image with alt text: x right arrow negative infinity and Image with alt text: f left parenthesis x right parenthesis right arrow negative infinity as Image with alt text: x right arrow infinity
f left parenthesis x right parenthesis right arrow infinity as x right arrow negative infinity and f left parenthesis x right parenthesis right arrow negative infinity as x right arrow infinity
Image with alt text: f left parenthesis x right parenthesis right arrow infinity as Image with alt text: x right arrow negative infinity and Image with alt text: f left parenthesis x right parenthesis right arrow negative infinity as Image with alt text: x right arrow infinity
f left parenthesis x right parenthesis right arrow negative infinity as x right arrow negative infinity and f left parenthesis x right parenthesis right arrow infinity as x right arrow infinity
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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.
1. 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, \( f(x) \to -\infty \).
2. 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**.
The leading term of a polynomial function dominates the end behavior as \( x \) approaches positive or negative infinity.
1. 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, \( f(x) \to -\infty \).
2. 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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