Unit 3

Polynomial, Radical, and Rational Functions

Analyze polynomial and rational functions including end behavior, zeros, asymptotes, and graphing techniques.

Unit 3 · 11 pages

Lessons

Unit overview, essential questions, learning objectives, and vocabulary list for Unit 3 Polynomial & Rational Functions.

Perform arithmetic with complex numbers, simplify powers of i, and find complex conjugates.

Write quadratics in vertex form, identify vertex and axis of symmetry, and solve using the quadratic formula.

Identify degree, leading coefficient, and end behavior of polynomial functions.

Find zeros, multiplicity, turning points, and sketch graphs of polynomial functions.

Divide polynomials using long division and synthetic division; apply the Remainder Theorem.

Apply the Rational Zero Theorem, Descartes' Rule of Signs, and the Fundamental Theorem of Algebra.

Find vertical, horizontal, and oblique asymptotes; graph rational functions and identify holes.

Find inverses of polynomial and radical functions; restrict domains to ensure invertibility.

Write and solve direct, inverse, and joint variation equations from real-world contexts.

Consolidate your understanding of polynomial and rational functions, zeros, asymptotes, and variation.