# How to reflect plot function toward $y=x$ with Plots?
**URL:** https://discourse.julialang.org/t/how-to-reflect-plot-function-toward-y-x-with-plots/95647
**Category:** General Usage
**Tags:** plotting
**Created:** [March 7, 2023, 4:56am UTC](https://discourse.julialang.org/t/how-to-reflect-plot-function-toward-y-x-with-plots/95647 "2023-03-07T04:56:29Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@Freya\_the\_Goddess](https://discourse.julialang.org/u/Freya_the_Goddess)
#### Post date: [March 7, 2023, 4:56am UTC](https://discourse.julialang.org/t/how-to-reflect-plot-function-toward-y-x-with-plots/95647/1 "2023-03-07T04:56:29Z")
Hi all,
I have the code from previous forum I made, that reflect a graph toward y axis. Now I want to reflect it toward y=x , I can’t just do `yreflection = y -> x` it prompts a lot of errors
This code works on y axis reflection.
```julia
using Plots, LaTeXStrings, Plots.PlotMeasures
gr()
function make_fg_plot()
f(x) = log(6x)
g(x) = 2x + log(6x)
yshift = y -> y + 0
yreflection = y -> y
ytransform = yshift ∘ yreflection
plt = plot(; xtick=:false, ylims = (-15, 15),
legend = :topleft, bottom_margin=5mm)
for (T, attrs) in [(identity, (;label = "", linecolor = :green)),
(ytransform, (;label = "", linecolor = :red))]
plot!(plt, T ∘ f, 0, 10; label="")
plot!(plt, T ∘ g, 0, 10; label="")
for i=0:0.2:2
plot!(plt, [2+i, 2+i], T.([f(2+i), g(2+i)]); label="")
end
annotate!([(3,-16.1, (L"x", 10, :black))])
annotate!([(3,-15.1, (L"|", 10, :black))])
end
return plt
end
make_fg_plot()
```
---
### Author:  [@Sevi](https://discourse.julialang.org/u/Sevi)
#### Post date: [March 7, 2023, 9:07am UTC](https://discourse.julialang.org/t/how-to-reflect-plot-function-toward-y-x-with-plots/95647/2 "2023-03-07T09:07:34Z")
Hi!
Thanks for the example code. Could you clarify what it _should_ be doing? Because it doesn’t reflect the functions at the y axis, as far as I can tell. Did you mean to write
```julia
yreflection = y -> -y
```
perhaps?
Regarding the question: Doing `yreflection = y -> x` will not do the right thing, because `x` is not known to this “reflection function”. What we are using here are _anonymous functions_ (you can read more about them here [Functions · The Julia Language](https://docs.julialang.org/en/v1/manual/functions/#man-anonymous-functions) ) and they are basically normal Julia functions, just without a name. So the function you intuitively wrote down would be something like
```julia
begin (y)
return x
end
```
but of course, `x` is not defined anywhere in the code, so it doesn’t know how to use it.
* * *
The transformation you want is only possible if we know the pair of coordinates (x, y) and make a function like `reflect_at_45 = (x, y) -> (y, x)`. But then the syntax for the plot would have to change and we would need to pass the range of `x` values explicitly, for example like so:
```julia
# Define the x-range explicitly
xrange = 0.0:0.1:10.0
# Define the transform (or anything else like `(x,y) -> (x, -y)` etc.
xyidentity = (x,y) -> (x,y)
xytransform = (x,y) -> (y, x)
...
for (T, attrs) in [(xyidentity, (;label = "", linecolor = :green)),
(xytransform, (;label = "", linecolor = :red))]
# Apply the transformation to all tuples (x, f(x))
transformedPoints = T.(xrange, f.(xrange))
# Make vectors out of the resulting tuples for plotting
newx = first.(transformedPoints)
newy = last.(transformedPoints)
plot!(plt, newx, newy; label="")
...
end
```
There is probably a simpler way of writing it than in my example, but it should be flexible enough to to any kind of reflections in 2D.
---
### Author:  [@Freya\_the\_Goddess](https://discourse.julialang.org/u/Freya_the_Goddess)
#### Post date: [March 7, 2023, 9:22am UTC](https://discourse.julialang.org/t/how-to-reflect-plot-function-toward-y-x-with-plots/95647/3 "2023-03-07T09:22:58Z")
Hi @Sevi ,
the code should reflect the graphs toward y=0 axis. This is the plot:
I give the bars to make it looks like Pharaoh
---
### Author:  [@Sevi](https://discourse.julialang.org/u/Sevi)
#### Post date: [March 7, 2023, 9:37am UTC](https://discourse.julialang.org/t/how-to-reflect-plot-function-toward-y-x-with-plots/95647/4 "2023-03-07T09:37:05Z")
> [@Freya\_the\_Goddess](#):
>
> ` yreflection = y -> y`
I just meant that the reflection in your example code is the same as `identity`. So when I run it, I just get the upper half of the plot, not the lower one. But it’s just a missing minus sign 🙂
---
### Author:  [@Freya\_the\_Goddess](https://discourse.julialang.org/u/Freya_the_Goddess)
#### Post date: [March 7, 2023, 12:21pm UTC](https://discourse.julialang.org/t/how-to-reflect-plot-function-toward-y-x-with-plots/95647/5 "2023-03-07T12:21:02Z")
I am able to create it like this:
with this code:
```julia
using Plots, LaTeXStrings, Plots.PlotMeasures
gr()
# Define the x-range explicitly
xrange = 0.0:0.1:20.0
# Define the transform (or anything else like `(x,y) -> (x, -y)` etc.
xyidentity = (x,y) -> (x,y)
xytransform = (x,y) -> (y, x)
function make_fg_plot()
f(x) = log(x)
plt = plot(; xtick=:true, xlims = (-15,15), ylims = (-15, 15),
legend = :topleft, bottom_margin=5mm)
for (T, attrs) in [(xyidentity, (;label = "", linecolor = :green)),
(xytransform, (;label = "", linecolor = :red))]
# Apply the transformation to all tuples (x, f(x))
transformedPoints = T.(xrange, f.(xrange))
# Make vectors out of the resulting tuples for plotting
newx = first.(transformedPoints)
newy = last.(transformedPoints)
plot!(plt, newx, newy; label="")
g(x)=x
plot!(g,linecolor=:green, line=(:dash), label="")
end
return plt
end
make_fg_plot()
```
thanks a lot!