Question

Is there a simple definition for what a function is? It's when a vertical line can pass through 2 points right?

Answer 1

a function relates a set of input with the set of permissible outputs

Answer 2

and each input has exactly one output

Answer 3

a function need not be a straight line

Answer 4

for each input (like x), there can be only one output (like y). If a vertical crosses more than one point on the graph, then the graph is NOT a function because it shows that an x value has more than one y value.

Answer 5

If any vertical line passes through more than one point of the graph then for some value of x there is more than one value of y.

Answer 6

so the value increases?

Answer 7

Is there a simple definition for what a function is? It's when a vertical line can pass through 2 points right?

It's the other way round: If a vertical line passes through two points of a curve, that curve does NOT represent a function. A vertical line has one x value. If it passes through two points on a curve that means the curve has the points (x,y1) and (x,y2) , two different y values for the same x. We want a curve with only 1 y value at each x, that way if you tell me x, I can tell you y. (If we had a choice of y's we don't have this nice rule)