This book helps students learn and connect topics more efficiently. It also helps teachers communicate topics more clearly. Even good students can be confused by higher level algebra topics by the way they are presented in textbooks, which is very technical and, at times, disconnected. This book translates and connects all those topics in great clarity.
It contains detailed definitions, explanations, step-by-step procedures, and covers the following topics:
FUNCTIONS
-Even & Odd
-Constant
-Composite
-Decomposing
-Inverse
-Reciprocal
-Difference Quotient of a Function
SYMMETRY With Respect To
-The y-axis
-The x-axis
-The Origin
-The diagonal line "y = x"
TRANSFORMATIONS
-Shifts
-Translations
-Reflections
-Stretching & Shrinking
-What is c?
HIGHER DEGREE POLYNOMIALS
-End Behavior
-Turning Points
-Multiplicity (Even or Odd Multiplicities of Zero)
-What are k & r?
-Successive Synthetic Division
-Graphing a Higher Degree Polynomial Function
THEOREMS IN WORDS
-The Extreme Value Theorem
-The Intermediate Value Theorem
-The Remainder Theorem
-The Factor Theorem
-The Rational Zero (p over q) Theorem
-Properties of Roots of Polynomial Equations
-The Factor Theorem
-The Fundamental Theorem of Algebra
-The Linear Factorization Theorem
-Descartes' Rule of Signs
ASYMPTOTES
-Vertical
-Horizontal
-Diagonal (a.k.a. Oblique)
GRAPHING A RATIONAL FUNCTION (including ASYMPTOTES)
EXPONENTIAL GROWTH vs. LOGISTIC GROWTH
SOLVING SYSTEMS OF (NONLINEAR) EQUATIONS
SOLVING SYSTEMS OF POLYNOMIAL INEQUALITIES
DETERMINATION OF A QUADRATIC EQUATION (a, b & c) GIVEN 3 POINTS
This book contains HYPERLINKS for easy, one-click topic jumping.
Please note, this book contains no trigonometry or calculus, but contains the prerequisite topics needed for those classes.

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