Questions and Answers
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?
In odd and positive end behavior, the function approaches +∞ at both ends.
False
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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Description
Explore the concept of end behavior in algebra, focusing on how polynomial functions behave as the input variable approaches positive or negative infinity. Understand the differences between even and odd functions in context with their leading coefficients and what influences their direction at the extremes.
