Question

Help?

In your own words, explain how to tell if a relation is a function and give an example.

Answer 1

A function is many-to-one relation. Have you heard it described that way before?

Answer 2

Basically a "function" works like this: You take one piece of INPUT, "do something to it", and then the result is your OUTPUT.

Usually in math functions are written like f(x) = 2x + 1 In this case the INPUT "is any real number x" the "Do something to it" is "take the number, multiply it by two, and then add one to that." The OUTPUT is ... whatever number is the result of the computation (2 times the number plus one).

So specifically let's say the INPUT is the number 3.
We "do something to the input"
2 times (3) plus 1 = 6 + 1 = 7
The OUTPUT is 7.

We know this is a function because each input goes to exactly one output.

Something that is not a function would be y^2 +x^2 = 1
You can solve this for y, (or x, it doesn't matter really) but... because of the square root, you have a single input going to different outputs.

y = PLUS or MINUS sqrt( 1 - x^2)

So if the INPUT is x = 1 the OUTPUT could be y = PLUS 1 o
OR
y = NEGATIVE 1

We have a single input (x = 1) going to TWO outputs (y = +1 or -1) That is NOT a function.
A function is where a single input goes to a single output.

Hope this helps.

Answer 3

Oh man, I made an error.


====================
This is how it SHOULD read
====================

So if the INPUT is x = 0 the OUTPUT could be y = PLUS 1 o
OR
y = NEGATIVE 1

We have a single input (x = 0) going to TWO outputs (y = +1 or -1) That is NOT a function.

Sorry 'bout that.