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