Understanding how polynomial functions behave at their ends can help us read their graphs better. Here’s a simple breakdown:

• Even-Degree Polynomials: The ends of the graph point in the same direction.

  • If the leading number (leading coefficient) is positive, both ends of the graph go up.
  • If it’s negative, both ends go down.

• Odd-Degree Polynomials: The ends of the graph point in opposite directions.

  • If the leading number is positive, the left side goes down and the right side goes up.
  • If it’s negative, the left side goes up and the right side goes down.

This information can really help you draw the general shape of the graph and guess where it might turn. Knowing this makes a big difference in how you tackle graphing!