Functions

[rachelmaddie]

I need my explanation checked for this please.
If a vertical line intersects the graph more than once, then the relation that the graph represents is not a function.It does not pass the “vertical line test”, which requires all vertical lines to intersect the graph at one point. Since a vertical line touches the relation at two points (1, 1) and (1, 3) at x = 1 this is not a function.

 

[tkhunny]

This is not correct: " requires all vertical lines to intersect the graph at one point ". Tell me why.

 

[rachelmaddie]

This is not correct: " requires all vertical lines to intersect the graph at one point ". Tell me why.

I mean “ if the vertical line only touches the graph at one point, then it is a function.”

 

[pka]

I mean “ if the vertical line only touches the graph at one point, then it is a function.”

Looking at the graph in #10 do you agree that both points \((1,1)~\&~(1,3)\) are on the graph?
Well there are two pairs with the same second(the vertical coordinate). So is that possible with a function?

 

[rachelmaddie]

Looking at the graph in #10 do you agree that both points \((1,1)~\&~(1,3)\) are on the graph?
Well there are two pairs with the same second(the vertical coordinate). So is that possible with a function?

No?

 

[Dr.Peterson]

The point is that your answer was correct, but your statement "which requires all vertical lines to intersect the graph at one point" is just a little off. It is not necessary for all vertical lines to intersect it at all; so you should properly say something like "every vertical line must intersect the graph in at most one point".

 

[yoscar04]

From Spivak's book on Calculus