You are not logged in.
Pages: 1
Why does y = f(x)?
For example, y = x + 2 can be written as f(x) = x + 2.
Why do we use f(x) to represent a function?
If y = f(x), can we say (x, y) = (x, f(x))?
Offline
Sure, it is correct: (x, y) = (x, f(x)).
We say y = f(x) because, worldwide, we agree on the convention that x is the independent variable (i.e., pick a value for x), and y is the dependent variable, because when we write y = f(x), or, e.g., y = 2x+5, the value of y depends on the value of x we picked.
Some algebra books have a few sections where we consider x = f(y). All graphs are turned sideways, vertical line tests become horizontal line tests, etc.
But the convention as noted above allows us to share our math. Nothing magical about y = f(x) - we just all agree to do it that way.
That help?
World Peace Thru Frisbee
Offline
If y=x+2 we can write y=f(x)=x+2
If y=h+2 we can write y=f(h)=h+2
If z=w+2 we can write z=f(w)=w+2
...
In brief, the notation f(a) means that we have a function (its name could be any symbol) in which the 'independent' variable is 'a'.
For example:
If y=3*x+2*a +1 and we read y=f(a), it means that 'x' here is not the independent variable of 'y', it is just added aa a parameter. In this case, we plot 'y' versus 'a', for each value of the parameter 'x' of interest. But saying y=f(x), 'x' is the independent variable and 'a' is the parameter in 'y'.
Offline
If y=x+2 we can write y=f(x)=x+2
If y=h+2 we can write y=f(h)=h+2
If z=w+2 we can write z=f(w)=w+2
...
In brief, the notation f(a) means that we have a function (its name could be any symbol) in which the 'independent' variable is 'a'.
For example:
If y=3*x+2*a +1 and we read y=f(a), it means that 'x' here is not the independent variable of 'y', it is just added aa a parameter. In this case, we plot 'y' versus 'a', for each value of the parameter 'x' of interest. But saying y=f(x), 'x' is the independent variable and 'a' is the parameter in 'y'.
Interesting. Thank you for your time.
Offline
Pages: 1