# Function Notation

## Key Questions

• An equation is an equality which is satisfied by a unique set of values of your variables. You have, after the $=$ sign a fixed value, a fixed result.

For example: the equation $4 x - 2 = 0$ has zero as result and only $x = \frac{1}{2}$ as solution; this means that if you substitute the value of $x = \frac{1}{2}$ in the equation you have the result zero, i.e., the equation is satisfied.

Now, a function is similar, the only difference is that now you can have a lot of results after the $=$ sign and so you can have a lot of solutions.

For example: the function $4 x - 2 = y$ doesn't have a definite result (as before that was zero) but another variable $y$, so every time you choose an $x$ you'll get the corresponding value of $y$ that satisfies it.
If you choose:
$x = 1 \to y = 2$
$x = 2 \to y = 6$
....etc.

If $x = \frac{1}{2} \to y = 0$ which is the solution that we found before for our specific equation (in which the $y$ was already set as zero)!

So to summarize, an equation has a fixed result (after the $=$ sign) and an unique set of solutions (values of the variables); a function can have a lot of results (possibly $\infty$) and, as a consequence, a lot of solutions.

hope it helps

I tried this:

#### Explanation:

Consider a Function ; this is a Rule, a Law that tells us how a number is related to another...(this is very simplified). A function normally relates a chosen value of $x$ to a determinate value of $y$.

Consider as an example a vending machine: you put, say 1$, and you get a can of soda... Our vending machine is relating money and soda. Now you can put the amount you like (1, 2, 3...$) BUT when you put a certain amount the result is only one...I mean if you put 1$ you get a soda nothing else...if you want a sandwich you need another amount. The amount of money you put depends upon you while the product is fixed; so the amount of money is INDEPENDENT (you put what you want) the resulting product given by the machine (once you decided) is DEPENDENT upon the amount you put in. For our mathematical function, once you choose a value for $x$the corresponding value of $y\$ DEPENDS upon this choice…

Hope I didn't confuse you even more...

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