Difference between f(x) and f(x,y)?
Andrew Mclaughlin 
I recently started doing calculus and came across terms such as f(x) and f(x,y). What is the difference between them? Are they the same thing?
$\endgroup$3 Answers
$\begingroup$$f(x)$ is a function of a single variable. For example, $f(x)=x^2$
$f(x,y)$ is a function of two variables. For example, $f(x)=x^2y+xy$.
$\endgroup$ $\begingroup$No, they are not the same thing. $f(x,y)$ is a function of two variables $x$ and $y$, e.g., $f(x,y) = 3x + \sin(y)$. But $f(x)$ is a function of only one variable, e.g., $f(x) = x^3$.
$\endgroup$ $\begingroup$In higher-level calculus, functions have multiple variables plugged into them and are charted using $(x,y,z)$! For example, if you wanted to graph the height of your driveway, you could use $h(w,l)$ where $w$ is a point on the width and $l$ is a point on the length. Check out Wolfram|Alpha for more of that stuff. They'll even let you try graphing some of your own $x$-$y$-$z$ functions!
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