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

In summary, if a line parallel to the x-axis intersects a graph at only one point, it indicates a one to one function. This is true for all lines parallel to the x-axis, meaning each input has a unique output value. This can be better understood through visual representation.
  • #1
#neutrino
51
2
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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  • #2
#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.
 
  • #3
what do you exactly mean by all lines ?
 
  • #4
#neutrino said:
what do you exactly mean by all lines ?
All lines parallel to the x- axis.
 
  • #5
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 ?
 
  • #6
#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.
 
  • #7
thanks , got it now
 

1. What is a 1-1 function?

A 1-1 function, also known as a one-to-one function, is a type of mathematical function where each element in the domain is mapped to a unique element in the range. In other words, each input has only one corresponding output.

2. How can you tell if a line intersects at one point?

A line will intersect at one point if it has a slope (or rate of change) that is different from the slope of any other lines it intersects. In other words, if two lines have different slopes, they will intersect at exactly one point.

3. Is there a difference between a line intersecting at one point and a 1-1 function?

Yes, there is a difference. A line intersecting at one point refers to the physical intersection of two lines, while a 1-1 function refers to the mathematical relationship between the input and output values of a function. A line intersecting at one point does not necessarily mean it is a 1-1 function, as it could intersect with multiple points on another line.

4. Can a line intersect at more than one point and still be a 1-1 function?

No, a line cannot intersect at more than one point and still be a 1-1 function. By definition, a 1-1 function must have a unique output for every input, so if a line intersects at multiple points, it would violate this rule.

5. How can you prove that a line intersecting at one point is a 1-1 function?

To prove that a line intersecting at one point is a 1-1 function, you would need to show that each input has a unique output. This can be done by using the slope-intercept form of a line (y = mx + b) and substituting in different values for x. If each x-value produces a different y-value, then the line is a 1-1 function.

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