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

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A line intersecting a graph at one point for every line parallel to the x-axis indicates that the function is one-to-one. If a horizontal line intersects the graph only once at a specific y-value, it confirms that each x-value corresponds to a unique y-value. This means that no two different x-values can produce the same output. The discussion emphasizes the importance of this condition for determining the one-to-one nature of a function. Visual representation can aid in understanding this concept better.
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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 ?
 
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#neutrino said:
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.
 
what do you exactly mean by all lines ?
 
#neutrino said:
what do you exactly mean by all lines ?
All lines parallel to the x- axis.
 
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 ?
 
#neutrino said:
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.
 
thanks , got it now
 

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