How can we know whether an equation is a function or not?

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How can we know whether an equation is a function or not?

OCW Scholar - Physics I: Classical Mechanics
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A function gives you one and only one 'y' value for a specific 'x' value. f(x)=x+1 is a function. If we take the equation of a circle \[x^{2}+y^2=r^2\] it's not a function because we can have two values 'y' for one 'x'. |dw:1359894319590:dw| P1(x1, y1) P2(x1, y2)
if we have the graph of a function we can do a simple geometric test called the vertical line test. It says that if a graph of a function then you will be able to draw a vertical line anywhere on that curve and it will only intersect at one point. This is a graphical representation of the idea that a function has only one input for every output, or, to say it another way, that there is only one y for every x. In this case it is obviously not a function by this definition.
Hello Akshayb. It's easy to difference between equations and functions. Equation: In an equation there's a unique value for each x, y... Per example: \[x + 3 = 2y\] and \[y - 1 = x\]In this given equation, values for x and y are uniques ( x = 1 and y = 2). You cannot change values because you won't get an equality... (trying with x=0 and y=5)\[0 + 3 \neq 2\times5\] Function: in a function, there are infinite values for x, y... Per example: (s = speed, l = lenght in meters, t = time in seconds) Wich is my speed rate if i reach goal of 100m in 15 seconds? \[s = \frac{ l }{ t }\] So... \[s = \frac{ 100 }{ 15 } = 6,7\] 6,7 meters per second is your speed (given values 100 for lenght and 15 for time). And what if you reach it in 10 seconds, or 7 seconds or... 'x' seconds? As you can see, the value of 's' depends on the values of distance and time and you can change values all the time. That's a function. I hope this post was useful ;)

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