Question 142821: which of these sets represents a function?..
(2,-2,), (3, -2), (2,3) or
(9,pie), (5,7), (4,pie) or
both or neither
PS: When I say pie I mean the 3.14 sign thing...: which of these sets represents a function?..
(2,-2,), (3, -2), (2,3) or
(9,pie), (5,7), (4,pie) or
both or neither
PS: When I say pie I mean the 3.14 sign thing...
Answer by nabla(409)  (Show Source):
You can put this solution on YOUR website!Functions must pass the vertical line test, which is to say that they must not be multi-valued per x. Thus, having points sharing x coordinates with different y coordinates is a no-no.
Your answer is, from the reasoning I have supplied, the first choice (2,-2,), (3, -2), (2,3) because x=2 is multi-valued. For a counter-example, consider the simple graph of f(x)=x^2. This is obviously a function. But, as you can see by the graph, different x values take on the same y values (namely, their opposites):
(-2)^2=2^2=4
By the way, pi is probably the most important mathematical constant there is. It represents the ratio of a circle's circumference to its diameter. That is, how long it is around over how wide it is. For future mathematical applications it's probably best to memorize it to, say, 5 decimal places. pi=3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510...
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