Which of the following sets of ordered pairs is not a function?

{(0, 2), (1, 4), (2, 5), (3, 6)}

{(-1, 2), (1, 3), (1, 5), (-3, 4)}

{(0, 2), (1, 2), (2, 2), (3, 2)}

{(-4, 3), (-1, 1), (-2, 5), (3, 7)}

Question

Which of the following sets of ordered pairs is not a function?



{(0, 2), (1, 4), (2, 5), (3, 6)}

{(-1, 2), (1, 3), (1, 5), (-3, 4)}

{(0, 2), (1, 2), (2, 2), (3, 2)}

{(-4, 3), (-1, 1), (-2, 5), (3, 7)}

lukebluefive · Answer

The ordered pairs are of the form (x, y).
A function is of the form y = mx + b.
One of these ordered pairs does not output a consistent value for y for each value of x.

lukebluefive · Answer

By definition a function must always return the same value for a given input.  One of these ordered pairs doesn't follow that rule.

mackenzie2013 · Answer

ok, so the numbers in parenthese are X and Y

lukebluefive · Answer

Yes, each parenthesis contains an x value and a y value.

mackenzie2013 · Answer

So how do you find out which is which?

lukebluefive · Answer

The first one is the x value and the second one is the y value.
x values are inputs, y values are outputs.

mackenzie2013 · Answer

Oh ok so you just figure out if the input is somehoe related to the output?

lukebluefive · Answer

That's one way to find the answer.  If the output is related to the input, then it's definitely a function.  However, there's an odd function that you need to be aware of:
$$y = constant$$
This is still a function, even though it always returns the same value.

mackenzie2013 · Answer

Ok , how do I find the answer?

mackenzie2013 · Answer

Im pretty confused, I understa nd the Y and x thats about it..

lukebluefive · Answer

Well, that's understandable, since this is confusing.

Let me try to explain this slightly differently.  For a given input, a function has to output the same value each time.  So whether the function is:
$$y = 1$$
Or:
$$y=2x+1$$
So when x = 2, the first function will output 1, and the second function will output 5.
However, a non-function could output 3 when x = 2 one time, then -1 another time.  One of the ordered x, y pairs gives an example of this behavior (different y values for the same x value).

mackenzie2013 · Answer

oh okay . I think I get it

lukebluefive · Answer

I remember having problems understanding formulas myself, so don't worry if it hasn't clicked yet.  It took me a lot of time doing a lot of examples before it made sense.

mackenzie2013 · Answer

yeah! Its kinda confusing haha