Question

Question #2ae17

Answer 1

This is probably debatable. Expressions are somewhat implicit because you need to be told what to do with them. Functions on the other hand are very explicit; it tells you what it needs and it will give you something back.

Remember that math is a language so it has rules (a lot of them). "5" is an expression. So, what's the answer?

• positive?
• odd?
• prime?
• part of the Fibonacci sequence?
• the number before 6?
• half of 10?

So giving an expression without context can be meaningless.

You've seen this a thousand times: `y=x^2+2x+7`. Is it an equation or a function? Again, it depends on the context. If this is all you are given, then you likely to treat this as a function, that is, `y(x)=x^2+2x+7`. However, if I also give you `y=-x^2-3x+20` then you have a system of linear equations.

To be properly define a function, it should always be defined with the function name and its parameters:

`f(x)=3x^4-5x^2`
`sin(theta)=...`
`g(x,y)=3sin(x)+4cos(y)`

Now, if we define something like:

`f(x)=alpha x^2+ beta x+ gamma`

We know, that the only variable (the thing that we can change) is `x`. The rest are just constants like `pi`. Maybe we know what they are, maybe we don't, but the function will give us a value back.

Yes, it's more work using function notation, but if everyone is clear about what's going on you can use the "=" sign.

I hope this is clear enough.