Polynomial functions are our “go to” functions. They are like decimal numbers for functions.

When you need to approximate a number, you select a decimal expansion with enough digits to give you the accuracy you desire. When you need to approximate a function, you select a polynomial with enough terms to give you the accuracy you desire.

We will do plenty of this approximating in Calculus.

So, we want to know everything about the analysis of polynomials.

• Domain
• Zeros

• Continuity

  • discontinuities
  • singularities
• End-Behavior

• Behavior

  • intervals where increasing
  • intervals where decreasing
• Global Maximum and Minimum
• Local Maximums and Minimums
• Range
• ...and we would like a nice graph

Learning Outcomes

In this section, students will

• paint a full picture of polynomials.
• use the Rational Roots Theorem.
• complete the picture of polynomials with the Fundamental Theorem of Algebra.