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Question 28798: How can you tell if a graph is that of a function?
((It would really help if this could be answered as soon as possible, because I have class in the morning... Thank you to anyone who answers.))
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website! How can you tell if a graph is that of a function?
((It would really help if this could be answered as soon as possible, because I have class in the morning... Thank you to anyone who answers.))
After drawing the graph(the diagram you have plotted I mean),
DRAW A VERTICAL LINE FROM ABOVE THE GRAPH POSITION TILL WELL INTO BELOW THE GRAPH.
If the vertical line cuts the graph at more than one point that means for the same abscissa you have more than one y-coordinate which is a taboo in a function because by definition of a function which is a rule that associates members of the first set(the domain set)with the members of the second set(codomain set)such that while EVERY member of the domain given an associate in the codomain, NO member can be given more than one associate, that is one single x can not have more than one image y.
This is the visual aid!
So any vertical line if it cuts the graph at only one point your diagram represents a graph of a function
Example: The entire diagram for (y)^2 = 4ax DOES NOT represent a function!
Either the upper part given by y=+[sqrt(4ax)] or the lower part given by
y=-[sqrt(4ax)] represents a function.
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