When you see this:

A. {(a, b), (a, c), (a, d), (a, e)}



Think  "x=a, y=b",  "x=a, y=c", "x=a, y=d", "x=a, y=e".



A function must have one value of y for each value of x, otherwise it does not meet the definition of 'function.'    In this example, do you see exactly one value of y for a given value of x?   No, because for x=a, y has 4 different values  (just having two different y values would be enough to disqualify it as a function).





Looking at case B, what do you think?  A function?   We see multiple occurrences of y=a, but each at different values of x.   This is OK for a function.  For example, look at the graph of a 4th order polynomial :









There are multiple places where y is the same value but that happens for different values of x.  If one dragged a vertical line along the x-axis, you would see it only intersects the graph once for each value of x that you pick. This is a function.





I will leave C to you.  Just remember  is by definition the principal square root of x  (i.e. the nonnegative square root only).    

















      

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