POLYNOMIAL, RATIONAL, EXPONENTIAL, AND LOGARITHMIC FUNCTIONS

College Algebra

The Factor Theorem

The factor theoremSolving polynomial equations

The Zeros of a Polynomial Function

The remainder theoremThe fundamental theorem of algebraThe rational root theorem

The Theory of Equations

The number of roots to a polynomial equationThe conjugate pairs theoremDescartes’ rule of signsBounds on the roots

Graphing Polynomial Functions

SymmetryBehavior at the x-interceptsSketching graphs of polynomial functions

Graphing Rational Functions

Rational functionsAsymptotes Sketching graphs of rational functions

Exponential Functions

Exponential functionsDomainGraphing exponential functionsTransformations of exponential functionsExponential equationsApplications

Logarithmic Functions

Logarithmic functionsDomain and rangeGraphing logarithmic functionsLogarithmic equationsApplications

Properties of Logarithms

Inverse propertiesProduct rule for logarithmsQuotient rule for logarithmsPower rule for logarithmsUsing the properties

Solving Equations

Logarithmic equationsExponential equationsChanging the baseStrategy for solving equationsApplications