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# Equations vs. functions

Equations and functions are not the same thing, but they can be related in several ways. Watch Jesse Roe and Sal talk about the difference between equations and functions. Created by Sal Khan.

## Want to join the conversation?

• if f(x) equals y then why bother use f(x).
• The following is from: http://www.purplemath.com/modules/fcnnot.htm
For functions, the two notations mean the exact same thing, but "f(x)" gives you more flexibility and more information. You used to say "y = 2x + 3; solve for y when x = –1". Now you say "f(x) = 2x + 3; find f(–1)" (pronounced as "f-of-x is 2x plus three; find f-of-negative-one"). You do exactly the same thing in either case: you plug in –1 for x, multiply by 2, and then add the 3, simplifying to get a final value of +1.

But function notation gives you greater flexibility than using just "y" for every formula. Your graphing calculator will list different functions as y1, y2, etc. In textbooks and when writing things out, we use names like f(x), g(x), h(x), s(t), etc. With this notation, you can now use more than one function at a time without confusing yourself or mixing up the formulas, wondering "Okay, which 'y' is this, anyway?" And the notation can be usefully explanatory: "A(r) = (pi)r2" indicates the area of a circle, while "C(r) = 2(pi)r" indicates the circumference. Both functions have the same plug-in variable (the "r"), but "A" reminds you that this is the formula for "area" and "C" reminds you that this is the formula for "circumference".
• What is a vertical line test ?
• A test to determine whether a relation is a function. When you graph a function (as Sal did at ), draw a vertical line at every point on the X axis (of course that's not practically possible, since there are infinite points, and besides, the whole paper would be black with lines - but do it in your head). If none of those vertical lines crosses the graph at more than one point, the relation is a function.
http://www.mathwords.com/v/v_assets/v11.gif
• arent linear equations technically functions?
• Most linear equations are functions. However, linear equations that create a vertical line would not be.
• when am I ever going to use this in my adulthood?
• How about when you go shopping and comparing prices, or when you a budgeting your money, paying bills, etc not to mention what applications it might have with your job.
• Instead of beating about the bush --A function has at least 2 variables: an output variable and one or more input variables. An equation states that two expressions are equal, and it may involve any number of variables (none, one, or more). A function can often be written as an equation, but not every equation is a function.
• FYI: Horizontal lines like y = 5 or f(x)=5 are functions but you only see the one variable in the equation. Thus, your first sentence is a little misleading. A function is a set ordered pairs where each input creates exactly one output. It does not need to be an equation. The equation for the functions does not need to have 2 variables. It just needs to be able to have / create ordered pairs that satisfy the rules for a function.
• Tell me if this question makes any sense: I noticed that using a graph was very affective in explaning what a function is. Can creating a graph resembling the one that was used in the video be the best way to solve it?
• yes making a graph to represent the one in the video is a good way to start out or at least that's what helped me
• What exactly is the difference between an equation and a function? As far as I could tell, Sal only gave examples of each and possible statements that could be made about equations or functions, but no clear definition as to what they are or the difference between them.
• A function is a set of ordered pairs where each input (x-value) relates to only one output (y-value). A function may or may not be an equation.

Equations are functions if they meet the definition of a function. But, there are equations that are not functions. For example, the equation of a circle is not a function.

This site might help: https://www.mathsisfun.com/sets/function.html
• what is one benefit of using functions?
• Functions have very many benefits, because functions have so many uses. As you learn more advanced forms of mathematics, you will find that functions can be used to simplify a concept or a statement. For example, 2x + 3 = y
One can say that a f(x), or a function of x, = y. So you can rewrite that equation as f(x) = 2x + 3. Now you can substitute "x" for any number you like. f(1) = 2(1) + 3. f(2) = 2(2) + 3. Hope this helped! Happy functioning!