Question 1142368
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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 {{{ y = x^4 -7*x^3 + 5*x^2 + 31*x - 30}}}:

{{{ graph(600,600,-6,6, -80, 80, y = x^4 -7*x^3 + 5*x^2 + 31*x - 30) }}}


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 {{{ sqrt(x) }}} is by definition the principal square root of x  (i.e. the nonnegative square root only).