3.1 Polynomial Functions

3.1 Polynomial Functions

Learning Intentions:

• I am learning how to identify the leading term and leading coefficient of a polynomial function
• I am learning how to identify the degree of a polynomial function algebraically
• I am learning how to identify the end behavior of a polynomial function

Success Criteria:

• I know I am successful when I can determine the leading term of a polynomial function and use that to determine the leading coefficient and end behavior of the function.

Parts of a polynomial:

f(x) = 5x4 + 3x3 - 2x2 + x + 9

• Terms
• Leading Term
• Degree
• Leading Coefficient

The degree of the polynomial is the greatest sum of exponents attached to the variables.

• x2 has a degree of 2;
• x2y3 has a degree of 5;
• (x2+xy2)2 would have a degree of 6

The degree also determines the end-behaviors of polynomial functions.

• An even degree value means the ends go in the same direction
• An odd degree value means the ends go in opposite directions

The constant value in the leading term is the leading coefficient, and determines if the function is increasing to infinity (positive coefficient), or decreasing to negative infinity (negative coefficient), as x goes to the right (positive infinity). As x -> positive infinity, y -> positive infinity.