Is a Line Intersecting at One Point a 1-1 Function?

[#neutrino]

if we draw a line parallel to the x- axis and passes through a point in the image and the graph intersects at one point is this a one to one function ?

 

[Samy_A]

if we draw a line parallel to the x- axis and passes through a point in the image and the graph intersects at one point is this a one to one function ?

If this is true for all lines parallel to the x-axis, yes.

 

[#neutrino]

what do you exactly mean by all lines ?

 

[Samy_A]

what do you exactly mean by all lines ?

All lines parallel to the x- axis.

 

[#neutrino]

but then for each line parallel to the x-axis for each input the output will be the same so how come it is one to one ?

 

[Samy_A]

but then for each line parallel to the x-axis for each input the output will be the same so how come it is one to one ?

No, a line parallel to the x-axis corresponds to a value of y.
If such a line, corresponding to the specific value $y_0$, intersects the graph of the function only once, it means that the function will have the value $y_0$ only once (for the $x_0$ corresponding to the intersection between the graph of the function and the line). If that is the case for all lines parallel to the x-axis, the function will be one to one.

Maybe you can draw it, that will make it clear I think.

 

[#neutrino]

thanks , got it now