Question 1142368: Please help me solve this:
Which of the following relations is a function / are functions?
A. {(a, b), (a, c), (a, d), (a, e)}
B. {(b, a), (c, a), (d, a), (e, a)}
C. {(1, 1), (2, sqrt(2)), (3, sqrt(3)), (4, 2)}
1. Only A
2. Only B
3. Only C
4. Only B and C
5. A, B
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website!
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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