# Thread: Graphing inverse that isn't reflected on y=x

1. ## Graphing inverse that isn't reflected on y=x

I know that inverse functions are supposed to be reflected about the line y=x. I hope this isn't a sleep deprived brain fart on my part, but when I graph y=-(1/2)x +3 and it's inverse, it is not reflected on that line.

Screenshot 2017-11-22 at 21.51.35.jpg

2. Originally Posted by thunc14
I know that inverse functions are supposed to be reflected about the line y=x. I hope this isn't a sleep deprived brain fart on my part, but when I graph y=-(1/2)x +3 and it's inverse, it is not reflected on that line.

Screenshot 2017-11-22 at 21.51.35.jpg
Your inverse is correct, and your graphs are correct, and the graph of the inverse IS the reflection of the original. You are apparently misinterpreting the graph or the idea of reflection. Can you explain what convinces you that it is not the reflection of the other line?

3. Originally Posted by Dr.Peterson
Your inverse is correct, and your graphs are correct, and the graph of the inverse IS the reflection of the original. You are apparently misinterpreting the graph or the idea of reflection. Can you explain what convinces you that it is not the reflection of the other line?
If I graph say y=2x+1 and it's inverse, y=x is clearly the axis of reflection, and then a line drawn from say (5,2) to (2,5) is orthogonal to y=x, and those points are an equal distance from that line.

Screenshot 2017-11-22 at 22.23.30.jpg

With my original equation does not show this relationship with y=x.

I was told y=x is always the axis of reflection with inverse functions. Is this wrong, or am I misunderstanding something here?

4. Originally Posted by thunc14
If I graph say y=2x+1 and it's inverse, y=x is clearly the axis of reflection, and then a line drawn from say (5,2) to (2,5) is orthogonal to y=x, and those points are an equal distance from that line.

Screenshot 2017-11-22 at 22.23.30.jpg

With my original equation does not show this relationship with y=x.

I was told y=x is always the axis of reflection with inverse functions. Is this wrong, or am I misunderstanding something here?
But your graphs do show the expected reflection. What pair of points do you say are not working?

The fact is that the line from any (a,b) to (b,a) will always be orthogonal to y=x; and this will always happen with an inverse function.

5. Here is your picture, with arrows added to show two points on one graph transformed to the corresponding points on the other [(0,6)-->(6,0) and (3,0) --> (0,3)].

Do you see how it is reflected in the line y=x?

Screenshot 2017-11-22 modified.jpg

6. Originally Posted by Dr.Peterson
Here is your picture, with arrows added to show two points on one graph transformed to the corresponding points on the other [(0,6)-->(6,0) and (3,0) --> (0,3)].

Do you see how it is reflected in the line y=x?

Screenshot 2017-11-22 modified.jpg
I assumed on first impression that the line of reflection would be in between the two line but with a negative slope. Your lines really helped point that out. Did you draw those on Desmos?

7. Originally Posted by thunc14
I assumed on first impression that the line of reflection would be in between the two line but with a negative slope. Your lines really helped point that out. Did you draw those on Desmos?
No, I just opened your picture in Paint and drew in the lines.

If you start with the lines, you can find two different lines of reflection, ONE of which is y=x. The fact that there is another line of reflection doesn't mean y = x is not one.

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