Plotting functions

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1. Dec 30, 2015

#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 ?

2. Dec 30, 2015

Samy_A

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

3. Dec 30, 2015

#neutrino

what do you exactly mean by all lines ?

4. Dec 30, 2015

Samy_A

All lines parallel to the x- axis.

5. Dec 30, 2015

#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 ?

6. Dec 30, 2015

Samy_A

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. Dec 30, 2015

#neutrino

thanks , got it now