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Which term of a polynomial decides its end behaviour?
AThe term of lowest degree
BThe term with no variable
CThe term with a negative sign
DThe term of highest degree
Answer & Solution
Correct answer: D. The term of highest degree
1. For very large or very small inputs, one term grows far faster than the rest.
2. That is the term with the highest power of the variable.
3. So the end behaviour of the whole polynomial matches the end behaviour of the term of highest degree.
4. The constant term shifts the graph but leaves the far left and far right unchanged.
_Source: OpenStax Precalculus (CC BY 4.0), section 3.3 Power Functions and Polynomial Functions_