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

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Discussion Overview

The discussion revolves around whether a line intersecting a graph at one point indicates that the function represented by the graph is a one-to-one function. The scope includes conceptual reasoning about functions and their properties.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants propose that if a line parallel to the x-axis intersects the graph at one point, it suggests that the function is one-to-one.
  • Others question the meaning of "all lines" and whether the same output for different inputs contradicts the definition of a one-to-one function.
  • A participant argues that if a line intersects the graph only once for a specific value of y, it indicates that the function has that value only once for the corresponding x, supporting the one-to-one claim.
  • One participant suggests that drawing the scenario might clarify the discussion.

Areas of Agreement / Disagreement

The discussion remains unresolved, with multiple competing views on the implications of a line intersecting the graph at one point and its relation to the one-to-one nature of the function.

Contextual Notes

Participants express uncertainty about the definitions and implications of one-to-one functions, particularly in relation to horizontal lines and their intersections with the graph.

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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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