# Lecture-5M.pptx - Mathematics Lecture u2013 5 Domain Range...

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MathematicsLecture – 5 / Domain & RangeFall Semester 2019Instructor:Brwa A. Saeed – MSc. Structural Engineering[email protected]Faculty of Engineering Tishk International University
Functions 2Lecture contents Domain and RangeNotations for domain and rangeDomain restrictionDomain of Purposely Restricted FunctionsDomain of rational functionsDomain of radical functionsDomain of both Rational and Radical FunctionsLecturer: A. S. Brwa – Faculty of Engineering – Calculus I – Lecture 5 –Domain and Range Tishk International University
Domain & Range 3Definitions of Domain & Range: Domain:is the set of all x values to which a function assigns a corresponding a real y value. Or the domain is the set of x-values where the function is defined (All input values of x).Range:is the set of all y values that result from x values. (All output values of y).Lecturer: A. S. Brwa – Faculty of Engineering – Calculus I – Lecture 5 –Domain and Range Tishk International University
Domain & Range 4Lecturer: A. S. Brwa – Faculty of Engineering – Calculus I – Lecture 5 –Domain and Range Tishk International University
Domain & Range 5Notations for Domain and RangeThere are three main notations to represent the domain or range. 1.Roster Notation:2.Set-Builder Notations:3.Interval Notation:Lecturer: A. S. Brwa – Faculty of Engineering – Calculus I – Lecture 5 –Domain and Range Tishk International University
Domain & Range 6Notations for Domain and Range1.Roster Notation:For Example:Determine the domain and range of the following set of ordered pairs. Lecturer: A. S. Brwa – Faculty of Engineering – Calculus I – Lecture 5 –Domain and Range Tishk International University
Domain & Range 7Notations for Domain and Range2.Set-Builder Notations: For Example: Lecturer: A. S. Brwa – Faculty of Engineering – Calculus I – Lecture 5 –Domain and Range Tishk International University
Domain & Range 8Notations for Domain and Range3.Interval Notation:Open brackets ( )Closed brackets [ ]One side open the other side is closed ( ] or [ ) (x, y)(2, 8)[2, 8] (2, 8] = 3, 4, 5, 6, 7 = 2, 3, 4, 5, 6, 7, 8 or [2, 8)= 3, 4, 5, 6, 7, 8 = 2, 3, 4, 5, 6, 7 Lecturer: A. S. Brwa – Faculty of Engineering – Calculus I – Lecture 5 –Domain and Range Tishk International University
Domain & Range 9Example – 1: Determine the Domain and Range for the following graphs of functions.