How Are Functions and Expressions Related?Date: 07/09/2004 at 11:05:49 From: Kristy Subject: relationships between functions and expressions What is the relationship between a function and an expression? I don't see any relationship, they are two completely different things. Date: 07/09/2004 at 11:42:44 From: Doctor Peterson Subject: Re: relationships between functions and expressions Hi, Kristy. Actually, I would say that they are almost exactly the same thing! But that may not be obvious. An expression is essentially the directions for a calculation, telling you to take this variable and that variable and do certain multiplications, additions, and so on. Right? Here's an example: 2x - y ------- 3x + 2y A function is a "machine" that takes one or more variables and does certain things to them to get a number out, which is the value of the function. Here is an example with one variable: f(x) = 3x - 4 Here is one with two variables: 2x - y f(x,y) = ------- 3x + 2y Look familiar? I can use any expression as the definition of a function, since the expression tells what to do with the variable(s) to get a value. On the other hand, not every function can be written as an expression using common operations. Here is a discussion of that fact, and other useful ideas about functions: Functions and Equations http://mathforum.org/library/drmath/view/53236.html See also: Are All Functions Equations? http://mathforum.org/library/drmath/view/53273.html The terminology all flows together sometimes. If you were given the equation 2x + 3y = 5 and I wanted you to "solve for y", I might instead tell you to "write an expression for y in terms of x" or to "write y as a function of x". These all mean the same thing, but focus on different aspects of what you are doing. "Solving" focuses on the equation as a problem, and the particular variable we want to find; "in terms of" focuses on which variable(s) are to be used in the calculation, rather than which is to be found; and "as a function" focuses on both. The latter is probably preferred by mathematicians for that reason, as well as for brevity. And brevity (the ability to talk about a big concept in a single word) is the main reason for defining "functions": Why Do We Have Functions? http://mathforum.org/library/drmath/view/62559.html If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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