inverse help (1 Viewer)

[yashbb]

how do i flip the graph over y=x. how do i know what the inverse graph should look like.
sorry its super dumb q

 

[ExtremelyBoredUser]

how do i flip the graph over y=x. how do i know what the inverse graph should look like.

This was a bit confusing to me at first but here's some techniques I've used in an exam scenario for graphing Inverse functions.

1. Tilt your paper so you are facing y=x, in that way you can see how to overlap more easier, just like how you would flip a graph on the y-axis.
2. Plot the x and y intercepts. The X,Y intercepts are switched from f(x) so a x intercept at 2 and 4 would be a y intercept at 2 and 4 for inverse function etc. This will make the inverse function more apparent
3. Try to graph the function of the inverse function if all else fails. Find the inverse function by swapping x,y etc. For example y=x^2 would have an inverse function of y = +-sqrt(x) and you could just draw a regular graph of sqrt x.

There's no real cheat or shortcut to graphing an inverse function, you just have to get used to it. I used desmos to get a more intuitive understanding:


This is perfect symmetry, if your teachers feeling nice they'll throw a cubic to graph.




Its just practice getting used to graphing inverse functions, there's not really much else to it. I just went through all the functions we covered for mx1 and graphed their inverse respectively and I was pretty much able to recognise the inverse. Sorry I don't really have a definite answer for this but its just something I feel you have to try to imagine.

 

[icycledough]

Is there like a sample question you have as an example? Because it is quite tricky to explain what you're asking without a question to work from. I mean deriving the equation is just switching the x and y terms, then forming the new equation in terms of y = f(x). However, with actually drawing the graph, it can help by rotating the paper where your graph is on so that the y = x line is vertical, rather than 45 degrees. Yh, I'm not too sure if that's the type of answer you were looking for. It's definitely not a dumb question, just a tricky one to explain through words without actually showing you.

 

[yashbb]

Is there like a sample question you have as an example? Because it is quite tricky to explain what you're asking without a question to work from. I mean deriving the equation is just switching the x and y terms, then forming the new equation in terms of y = f(x). However, with actually drawing the graph, it can help by rotating the paper where your graph is on so that the y = x line is vertical, rather than 45 degrees. Yh, I'm not too sure if that's the type of answer you were looking for. It's definitely not a dumb question, just a tricky one to explain through words without actually showing you.

can we take a really simple example of something like y=2x?

 

[Eagle Mum]

Pencil in your graphs (e.g. unbroken line for original curve & dotted line for the inverse graph). Place a mirror on the line y=x to check if your sketch of the 'flipped' graph matches the mirror image of the original curve.

You'll have to flip your mirror around (eg. first check all points with y<x and then flip mirror to check points y>x).

 

[yashbb]

Pencil in your graphs (e.g. unbroken line for original curve & dotted line for the inverse graph). Place a mirror on the line y=x to check if your sketch of the 'flipped' graph matches the mirror image of the original curve.

You'll have to flip your mirror around (eg. first check all points with y<x and then flip mirror to check points y>x).

i dont have a mirror in the exam

 

[Eagle Mum]

i dont have a mirror in the exam

Sorry - I meant whilst you were practising sketches.