Power and Polynomial Functions College Algebra Power Function

Power and Polynomial Functions College Algebra

Power Function •

End Behavior of Power Functions •

End Behavior of Power Functions with Even Power • •

End Behavior of Power Functions with Odd Power • •

Identifying the End Behavior of a Power Function EXAMPLE: IDENTIFYING THE END BEHAVIOR OF A POWER FUNCTION.

Desmos Interactives Topic: end behavior of power functions (Even powers) - https: //www. desmos. com/calculator/rgdspbzldy (Odd powers) - https: //www. desmos. com/calculator/4 aeczmnp 1 w

Polynomial Function •

Terminology of Polynomial Functions • We often rearrange polynomials so that the powers are descending • When a polynomial is written in this way, we say that it is in general form

End Behavior of Polynomial Functions •

Identifying End Behavior and Degree of a Polynomial Function

Local Behavior of Polynomial Functions •

Principle of Zero Products •

Intercepts of a Polynomial Function •

Multiplicity •

Example: Identifying Zeros and Their Multiplicities

Graphing Polynomial Functions •

Example: Sketching the Graph of a Polynomial Function

Example: Sketching the Graph of a Polynomial Function

Intermediate Value Theorem •

Factored Form of Polynomials •

Local and Global Extrema •

Desmos Interactive Topic: zeros from a graph with slider = a to change y-intercept https: //www. desmos. com/calculator/5 oyyx 0 vbiv

Division Algorithm •

Synthetic Division •

The Remainder Theorem • 2 6 6 − 15 12 22 11 7 2 14 16 − 7 32 25

The Rational Zero Theorem •

The Factor Theorem •

Find Zeros of a Polynomial Function •

Fundamental Theorem of Algebra •

Complex Conjugate Theorem •

Descartes’ Rule of Signs •

Quick Review •