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Study Guides > MATH 0123

Summary: Review

Key Concepts

  • A polynomial function is one whose equation contains only non-negative integer powers on the variable.
  • The polynomial term containing the highest power on the variable is the leading term, and its degree is the number of the power. The leading coefficient of a polynomial is the coefficient of the leading term.
  • The graph of a polynomial function describes a smooth, continuous curve.
  • The domain of all polynomial functions is all real numbers.
  • Even degree polynomial functions describe graphs whose ends both point up or both point down.
  • Odd degree polynomial functions describe graphs whose ends points in opposite directions.
  • The sign of the leading term will determine the direction of the ends of the graph:
    • even degree and positive coefficient: both ends point up
    • even degree and negative coefficient: both ends point down
    • odd degree and positive coefficient: the left-most end points down and the right-most end points up.
    • odd degree and negative coefficient: the left-most end points up and the right-most end points down.

Glossary

degree
the highest power of the polynomial
leading coefficient
the coefficient of the leading term
leading term
the term containing the highest power

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