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.
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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.
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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?
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?
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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?