I'm trying to combine 3 functions graphed on a Plot[] and 1 function graphed on a ParametricPlot[]. My equations are as follows:
plota = Plot[{-2 x, -2 Sqrt[x], -2 x^(3/5)}, {x, 0, 1}, PlotLegend -> {"-2 x", "-2 \!\(\*SqrtBox[\(x\)]\)", "-2 \!\(\*SuperscriptBox[\(x\), \(3/5\)]\)"}] plotb = ParametricPlot[{2.4056 (u - Sin[u]), 2.4056 (Cos[u] - 1)}, {u,0, 1.40138}, PlotLegend -> {"Problem 3"}] Show[plota, plotb] This is the image it gives:
As yoda said, PlotLegends is terrible. However, if you don't mind setting the plot styles manually and repeating them lateron, ShowLegend can help.
plota = Plot[{-2 x, -2 Sqrt[x], -2 x^(3/5)}, {x, 0, 1}, PlotStyle -> {{Red}, {Blue}, {Orange}}]; plotb = ParametricPlot[{2.4056 (u - Sin[u]), 2.4056 (Cos[u] - 1)}, {u, 0, 1.40138}, PlotStyle -> {{Black}}]; And now
ShowLegend[Show[plota, plotb], {{{Graphics[{Red, Line[{{0, 0}, {1, 0}}]}], Label1}, {Graphics[{Blue, Line[{{0, 0}, {1, 0}}]}], Label2}, {Graphics[{Orange, Line[{{0, 0}, {1, 0}}]}], Label3}, {Graphics[{Black, Line[{{0, 0}, {1, 0}}]}], Label4}}, LegendSize -> {0.5, 0.5}, LegendPosition -> {0.5, -0.2}}] which will give you this:
You can also write some simple functions to make this a little less cumbersome, if you deal with this problem often.
Well, the root cause of the error is the PlotLegends package, which is a terrible, buggy package. Removing that, Show combines them correctly:
plota = Plot[{-2 x, -2 Sqrt[x], -2 x^(3/5)}, {x, 0, 1}] plotb = ParametricPlot[{2.4056 (u - Sin[u]), 2.4056 (Cos[u] - 1)}, {u, 0, 1.40138}] Show[plota, plotb] 
You can see Simon's solution here for ideas to label your different curves without using PlotLegends. This answer by James also demonstrates why PlotLegends has the reputation it has...
You can still salvage something with the PlotLegends package. Here's an example using ShowLegends that you can modify to your tastes
colors = {Red, Green, Blue, Pink}; legends = {-2 x, -2 Sqrt[x], -2 x^(3/5), "Problem 3"}; plota = Plot[{-2 x, -2 Sqrt[x], -2 x^(3/5)}, {x, 0, 1}, PlotStyle -> colors[[1 ;; 3]]]; plotb = ParametricPlot[{2.4056 (u - Sin[u]), 2.4056 (Cos[u] - 1)}, {u, 0, 1.40138}, PlotStyle -> colors[[4]]]; ShowLegend[ Show[plota, plotb], {Table[{Graphics[{colors[[i]], Thick, Line[{{0, 0}, {1, 0}}]}], legends[[i]]}, {i, 4}], LegendPosition -> {0.4, -0.15}, LegendSpacing -> 0, LegendShadow -> None, LegendSize -> 0.6}] 
fns[x_] := notation he is using, because I have a parametric equation. Can you show me how to add labels? Also, I imported an image into my LaTeX document, but it was too big so I scaled it by .5, which made it look pretty crappy. How can I make it smaller and still look nice?
As the other answers pointed out, the culprit is PlotLegend. So, sometimes is useful to be able to roll your own plot legends:
plotStyle = {Red, Green, Blue}; labls = {"a", "b", "Let's go"}; f[i_, s_] := {Graphics[{plotStyle[[i]], Line[{{0, 0}, {1, 0}}]}, ImageSize -> {15, 10}], Style[labls[[i]], s]}; Plot[{Sin[x], Sin[2 x], Sin[3 x]}, {x, 0, 2 Pi}, PlotStyle -> plotStyle, Epilog -> Inset[Framed[Style@Column[{Grid[Table[f[i, 15], {i, 1, 3}]]}]], Offset[{-2, -2}, Scaled[{1, 1}]], {Right, Top}], PlotRangePadding -> 1 ] 
