Determine if the function is a one-to-one function: (Answer yes or no). f(x)= {–4, –2), (–3, 0), (–1, –5), (0, 4), (3, 10)}

Question

Determine if the function is a one-to-one function: (Answer yes or no).                                                                           f(x)= {–4, –2), (–3, 0), (–1, –5), (0, 4), (3, 10)}

anonymous · Answer

Wanna know the easy way to solve this?

anonymous · Answer

yes

anonymous · Answer

Please

anonymous · Answer

look at second numbers. if they repeat, not one to one. if they don't repeat, one to one.  that is all

anonymous · Answer

Sorry for taking so long.  Satellite is correct for the most part, but you've also gotta check the first numbers.  If there's any repeat in the first number where the second numbers are NOT the same for the first number, then it's NOT a function.

anonymous · Answer

i guess so but who writes functions with ordered pairs repeated? i suppose it is possible...

anonymous · Answer

In other words:

(1,0)  (2,0) (3,3) (4,6)
This one fails because there's two zeros.  It's a function, but the 0's repeat.

(1,3) (1,4) (4,5) (6,7)
This one fails because it's not a function, due to the first two pairs sharing a 1.. even though there's no repeats in the second numbers.

(3,2), (4,4) (5,6)
Passes because there's no repeat in either the first numbers, nor the second ones.  Note that the 4,4 doesn't count against us because we only care about repeats in the first numbers or the second numbers.

anonymous · Answer

Lets just define it properly.

A function is one to one if for any x, y in the domain:
f(x) = f(y) -> x = y

anonymous · Answer

Let's face it:  what algebra student will understand that notation?

anonymous · Answer

A linear algebra student will

anonymous · Answer

here is some notation.  a function given by a set of ordered pairs is one to one if the second numbers do not repeat.  fancy english language notation

anonymous · Answer

Yes but here in the math world we use formal logic.

anonymous · Answer

Implications and all that fancy stuff

anonymous · Answer

Sorry, I'm being a little silly. Just disregard what I've said.

anonymous · Answer

No problemo. :P  It's good to have fun and whatnot.  I mean I totally agree that in an academia field where math majors are mingling and trying to prove stuff a standard of mathematical proofs and whatnot should be used.  But here, I was just saying that most folks that ask questions would be thrown off by just seeing f(x) instead of y=