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Questions and Answers
What is end behavior?
What is end behavior?
The behavior of the graph as x approaches positive infinity or negative infinity.
What is the characteristic of even and negative end behavior?
What is the characteristic of even and negative end behavior?
- Both ends approach +∞ (correct)
- Both ends approach -∞ (correct)
- One end approaches +∞ and the other -∞
- None of the above
In odd and positive end behavior, the function approaches +∞ at both ends.
In odd and positive end behavior, the function approaches +∞ at both ends.
False (B)
In odd and negative end behavior, as x approaches -∞, f(x) approaches _____ and as x approaches +∞, f(x) approaches _____
In odd and negative end behavior, as x approaches -∞, f(x) approaches _____ and as x approaches +∞, f(x) approaches _____
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Study Notes
End Behavior in Algebra
- Refers to the behavior of a graph as the input variable x approaches positive or negative infinity.
- Essential for understanding how polynomial functions behave at their extremes.
Even and Negative End Behavior
- Both ends of the graph approach the same direction.
- Determined by the leading coefficient:
- If positive, both ends go to +∞.
- If negative, both ends go to −∞.
Odd and Positive End Behavior
- Graph exhibits opposite behavior at each end.
- Determined by the leading coefficient:
- If positive, as x approaches −∞, f(x) approaches −∞ and as x approaches +∞, f(x) approaches +∞.
Odd and Negative End Behavior
- As x approaches −∞, the function f(x) approaches +∞.
- As x approaches +∞, the function f(x) approaches −∞.
- Illustrates the contrasting behavior of the function at the two ends.
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