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Page 1: Functions

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

radical function, conditional function, zeroes of function

Page 2: Functions

FunctionCartesian Product

Page 3: Functions

FunctionCartesian Product

Page 4: Functions

FunctionCross Product

Page 5: Functions

FunctionCross Product

Page 6: Functions

FunctionCartesian Product

Page 7: Functions

FunctionCartesian Product

Page 8: Functions

FunctionCartesian Product

Page 9: Functions

FunctionDomain and Range, Graph

Functions generate graphs

But not all graphs are functions

Page 10: Functions

FunctionGraph, Vertical Line Test

Page 11: Functions

FunctionGraph, Vertical Line Test

Page 12: Functions

FunctionPolynomial Function

Polynomial functions are defined for all real numbers

𝐷 𝑓 =𝑅

Page 13: Functions

FunctionPolynomial functions examples

Page 14: Functions

FunctionExamples

Page 15: Functions

FunctionPolynomial functions, examples

Page 16: Functions

FunctionRational Function

Page 17: Functions

FunctionRational function, graph, domain

Page 18: Functions

FunctionRational function

Page 19: Functions

FunctionRational Function

Page 20: Functions

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

Page 21: Functions

FunctionRadical function

Page 22: Functions

FunctionZeroes of function (Roots)

Page 23: Functions

FunctionZeroes of function, roots

Page 24: Functions

FunctionsZeroes of functions

Page 25: Functions

FunctionsZeroes of functions

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

Page 26: Functions

FunctionFactor Theorem

Page 27: Functions

FunctionFactor Theorem

Page 28: Functions

FunctionFactor Theorem

Page 29: Functions

FunctionConditional function

Conditional function is also referred to as piece-wise function

Page 30: Functions

FunctionConditional function/piece-wise function

Page 31: Functions

FunctionConditional function/piece-wise function


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