Functions

FunctionsDefinition, domain, range, graph, polynomial, rational,

radical function, conditional function, zeroes of function

FunctionCartesian Product

FunctionCartesian Product

FunctionCross Product

FunctionCross Product

FunctionCartesian Product

FunctionCartesian Product

FunctionCartesian Product

FunctionDomain and Range, Graph

Functions generate graphs

But not all graphs are functions

FunctionGraph, Vertical Line Test

FunctionGraph, Vertical Line Test

FunctionPolynomial Function

Polynomial functions are defined for all real numbers

𝐷 𝑓 =𝑅

FunctionPolynomial functions examples

FunctionExamples

FunctionPolynomial functions, examples

FunctionRational Function

FunctionRational function, graph, domain

FunctionRational function

FunctionRational Function

FunctionRadical function

A radical function g is a function in the form

𝑔 (𝑥 )=𝑛√ 𝑓 (𝑥 )

𝐼𝑓 𝑛=2𝑘 ,𝑘∈𝑁 ,𝐷𝑔= {𝑥∨ 𝑓 (𝑥)≥0 }

𝑖𝑓 𝑛=2𝑘+1 ,𝑘∈𝑁 ,𝐷𝑔=𝑅

FunctionRadical function

FunctionZeroes of function (Roots)

FunctionZeroes of function, roots

FunctionsZeroes of functions

FunctionsZeroes of functions

It has exactly n roots in the set of complex numbers.

FunctionFactor Theorem

FunctionFactor Theorem

FunctionFactor Theorem

FunctionConditional function

Conditional function is also referred to as piece-wise function

FunctionConditional function/piece-wise function

FunctionConditional function/piece-wise function