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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))?
The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.
Dr. David Jeremiah
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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
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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'.
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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.
The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.
Dr. David Jeremiah
Offline
Pages: 1