mesa said:How would someone go about writing a general expression for a function of a single variable and a constant? For example, if we have a function of two variables 'x' and 'y' we can use f(x,y). If we had a function of 'x' and the constant '∏' is it acceptable to write it as f(x,π)?
Curious3141 said:Why would you want to do that? By definition, a constant does not change, so it should not influence the dependent variable.
Functions like ##x \rightarrow \pi x## or ##x \rightarrow \sin \pi x## are completely adequately represented as ##f(x)## (omitting the ##\pi##).
olivermsun said:There are lots of notations for a function ##f## in variable ##x## with some constant parameter ##a##, besides just plain old ##f(x, a).## Some other examples are ##f_a(x)##, ##f^{(a)}(x)##, ##f(x; a).##
HallsofIvy said:I have seen the notation f(x; c) used to indicate a function of the variable x which depends upon the parameter c. I think the word "parameter" is better here than "constant".
(You understand that the distinction between a "variable" and a "constant" that can take on different values is pretty slim!
f(x; c) is understood to mean a family of functions of x, each possible value of c giving a different function in that family.)
If it's just a constant like e then just don't put it.mesa said:On another note, for this particular instance I am interested in notation for a function of one variable that also happens to have a single known constant (e.g. π, or e, or phi, etc.) as part of that function. If I had a function of a single variable 'x' and constant '∏' is f(x,∏) an acceptable form to describe said function?
Only if there's no chance of confusion.Jorriss said:If it's just a constant like e then just don't put it.
Jorriss said:If it's just a constant like e then just don't put it.
It seems adequate. I've seen it in textbooks and published papers alike.mesa said:I understand this sentiment, however if it were that simple I wouldn't be here. Do you think using the form f(x,some constant) is adequate?
olivermsun said:It seems adequate. I've seen it in textbooks and published papers alike.
In this case you would write f(x) = lnx =log_e x. You're still not writing the e in the name of the function, f.olivermsun said:Only if there's no chance of confusion.
For example, I think writing ##\log_e(x)## and ##\log_{10}(x)## is a good idea when either or both could be used.
I prefer ## f_c(x) ## to indicate that the function is only a function of x.mesa said:I understand this sentiment, however if it were that simple I wouldn't be here. Do you think using the form f(x,some constant) is adequate?
You are. The ##e## appears in the subscript of the function name ##\log##. Anyway it's just one possible convention. The point is to distinguish between base ##e## and ##10## clearly.Jorriss said:In this case you would write f(x) = lnx =log_e x. You're still not writing the e in the name of the function, f.
Hm, yeah I suppose you're right about this one. Though a comment, even here you aren't using the notation ##f(x,a)##, it's still the notation ##f_a(x)##.olivermsun said:You are. The ##e## appears in the subscript of the function name ##\log##. Anyway it's just one possible convention. The point is to distinguish between base ##e## and ##10## clearly.
To write a function of a single variable and a constant, you would use the mathematical notation f(x) = ax + b, where a is the constant and x is the variable. This notation is called the slope-intercept form and is commonly used to express linear functions.
The constant in a function represents the y-intercept, which is the point where the function intersects with the y-axis. It is the value of the function when the variable is equal to 0.
No, a constant cannot be a variable in a function. A constant is a fixed value that does not change, while a variable is a value that can take on different values. It is important to distinguish between constants and variables in a function.
To graph a function with a single variable and a constant, you would plot the y-intercept on the y-axis and then use the slope to plot additional points on the graph. The slope is determined by the coefficient of the variable in the function.
Yes, a function can have more than one constant. In fact, a function can have multiple constants and multiple variables. Each constant would represent a different y-intercept, and each variable would have its own coefficient or slope.