[Music] hi class welcome back to our channel for this video discussion and about ebooks some functions and relations okay so define when nothing young relation a relation is any set of ordered pairs the set of all the x components of the ordered pairs is called the domain of the relation and the set of all the y components is called the range okay so if it's a bn a relation is a rule that relates values from a set of values called the domain okay to a second set of values called the range so whether nothing imagine domain is your adding input machine while syringe is so let's give the domain and range of the following relation for number one we have one three two four five seven and six comma eight x components of the ordered pairs okay so on only on we have one two five and six nahua while young range number is the set of all y components so you know we have seven then the sixth meron eight guys three four seven and eight so next number two so begin adding in domain and range again your adding domain is the set of all x components so you know numbers we have negative two negative one then multiply negative two so since mean negative two naught that is our y components so we have four one zero then five and last is your negative two okay so puerto ri nothing arranged guys human numbers are adding set from lowest to highest or highest lowest depending guys um a relation in which each member of the domain is paired to exactly one member of the range is called a function so on the banks of being none [Music] relation function if no two ordered pairs have the same x value but different y values function number one we have one two two three three four and four comma five so as you can see guys um input nothing is a function okay next number two we have one comma one then two comma two three comma three and four comma four so as you can see guys now you mean nothing is a unique output or is output so ebx bn young number to nothing is also a function okay next number three one zero zero one negative one zero and zero negative one okay so guys which is zero and zero domain is paired to exactly one member of the range so this time domain is okay which is one and negative one so therefore uh number three is not a function okay so next number four we have negative two four negative one one zero zero one one then two four okay so uh domain nothing which is negative two negative one zero one two is is a function guys okay next uh functions can also be represented through mapping okay so where the elements of the domain are map to the elements of the range using arrows okay so in this case uh the relation or function is represented by the set of all the connections by the arrows all right so try which of the following mapping diagrams represent function x component corresponds to a unique range tama young one corresponds to three two corresponds to five three corresponds to nine then four to seven then five to thirty three so latina input nathan is my unique output so therefore your number one nothing is a function okay so function n so next number two uh we have x u7 output near one you eat an output in a zero then your nine and output is zero all right so one problem guys okay so next number three naman meru 11 13 17 19 and 23. so guys 11 and 13. okay then at the same time your input not in the two is made in the output output okay so this time uh your input not in the seven meet the level output so eb sub n uh this function or this relation is not a function all right nine indian but guys you're adding uh mapping diagrams okay so i unmoved dials of functions as a graph in the cartesian plane all right so given the graph of a relation we can easily identify if it is a function or not by using the vertical line test okay so underneath vertical line test a graph of a mathematical relation is said to be a function if any vertical line drawn passing through the graph touches the graph at exactly one point all right so if it's a bn uh magicking function is a graph if i connect in a vertical line that is example so which of the graphs represent a function so letter a so little guys are to test the graph again the gamma line of vertical line okay so um in a vertical line so any point in graph in your guys represents a function okay so next number two or letter b so determination is straight line so this line represents a function this ellipse is not a function or this graph is not a function so that means uh this graph represents a function um so that means this type of hyperbola is not a function and so gangnam language simply guys give me the new outing vertical line this so this is the end of our video i hope uh 19 day and you guys go on about ebay subscribe and if you have questions or clarifications kindly put them in the comment section below thank you guys for watching this is prof d i'll catch you on the flip side bye