F(x) meaning clarification please

[Physicist3]

Hi,

This is probably really simple but it seems to be confusing me and I was wondering if someone could clarify if I am correct as to the use of f(x) please.

If you have an equation, say y=6x²+3x+4, does this equation then become f(x) so that y=f(x) and f(x) = 6x²+3x+4? Also, if you put a number into the brackets, does this mean that you replace the x's with this number? E.g. if the above equation became y=f(2), would this then mean that y = 6 * 2²+3*2+4 and y=f(2) would therefore = 34?

Thanks

 

[Mark44]

Hi,

This is probably really simple but it seems to be confusing me and I was wondering if someone could clarify if I am correct as to the use of f(x) please.

If you have an equation, say y=6x²+3x+4, does this equation then become f(x) so that y=f(x) and f(x) = 6x²+3x+4?

In your first equation, y is a function of x (in symbols, y = f(x)), so you could also say that f(x) = 6x²+3x+4.

Also, if you put a number into the brackets, does this mean that you replace the x's with this number?

Yes, the formula says how a function value should be computed.

You have f(x) = 6x²+3x+4, so if x = 2, then f(2) = 6(2)² + 3(2) + 4 = 34.

This means that the point (2, 34) is on the graph of the function. It also means that (1, 13) is on the graph, and that (0, 4) is on the graph.

E.g. if the above equation became y=f(2), would this then mean that y = 6 * 2²+3*2+4 and y=f(2) would therefore = 34?

Thanks

 

[Office_Shredder]

Everything is correct except for the phrase "does this equation then become". It is true that y is a function of x, and it is true that you can say "let f(x) =y" and then do things like f(2) = 34. It is not true that if someone writes down y=6x²+3x+4 that you can then say "therefore f(2) = 34" without anything in between and expect that to make sense - if all you are given is y=6x²+3x+4 then if you want to describe that function as being f(x) you have to explicitly say so.

You also don't want to write something like "y=34" as a standalone equation... you can include it as a sentence, like

When x=2, y=34

is OK, but if you just wrote

"Let y=f(x)=6x²+3x+4. Then y=f(2) gives y=34"
this would make no sense, because y is not equal to f(2) except for when x=2, and you have never actually stated that for y you are plugging in x=2 (even though it's obvious from what you wrote). I think in general if you are going to be evaluating y a lot it's best to just write let f(x) = 6x²+3x+4 and never refer to y again.

This might seem like nitpicking but when students are first learning these concepts I have often seen them confuse themselves into writing wrong things by trying to string together almost-but-not-quite correct statements with bad grammar.