Someone please give an example?
Give an example of a relation that is NOT a function and explain why it is not a function.

Question

Someone please give an example?
Give an example of a relation that is NOT a function and explain why it is not a function.

jim_thompson5910 · Answer

Any time when you have x mapping to more than one y value is when you won't have a function

anonymous · Answer

Um can you be a lil more specific?

jim_thompson5910 · Answer

say you had x = 2 mapping to y  = 1 and y = 4

this can't be a function because you would need to know the specific output y when you plug in some x

jim_thompson5910 · Answer

but if you plug in x = 2, you'll get y = 1 or y = 4..which one will pop out? there's no way of knowing

so that's why it's not a function

jim_thompson5910 · Answer

does that help?

jamesj · Answer

Here's another example:
$$ x^2 = y^2 $$

If you try and graph that relation, you will see that for every non-zero value of x there are two values of y and vice versa. Hence this relation can't be reduced to a single function.

anonymous · Answer

how about f(x) = sqrt(x).? Sooo every number has two square roots (positive and negative), so this wouldnt be a function right?

anonymous · Answer

i mean haha i didnt copy that or anything. i just came up with that myself.

jim_thompson5910 · Answer

f(x) = sqrt(x) is a function because plugging in any positive number for x will result in some single positive output

jim_thompson5910 · Answer

sure this equation x^2 = 4 has two solutions

BUT

sqrt(4) = 2 and not sqrt(4) = -2

anonymous · Answer

Ohhhh. okay! thanks!

jim_thompson5910 · Answer

what JamesJ was saying is that if you solve for y, you get

y = plus/minus sqrt(x^2)

y = plus/minus x

so if x = 3 for instance, then y is both positive 3 and negative 3 at the same time

this invalidates the fact that it's a function