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I have a function and $x$-values as a list. How do I construct a list with coordinates $(x_i,y(x_i))$, $i=1, 2, …$

y[x_]:= 2x
x = { -3, 0, 4, 5}

which should be made into

{ {-3,-6}, {0,0}, {4,8}, {5,10} }

Is there some compact command for this? The following works but is perhaps not optimal;

Table[{x[[i]], y[x][[i]]}, {i, 1, Length[x]}]
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    $\begingroup$ For example Table[{x, y[x]}, {x, xvalues}] where xvalues = {-3, 0, 4, 5}. This is probably the most semantically appealing option. Another solution is Transpose[{x, y /@ x}] where x is as you defined it. Those are general solutions, in your case you have a listable function, which means that you can also use the slightly simpler Transpose[{x, y[x]}], and if performance matters then this is what you should use. $\endgroup$
    – C. E.
    Jun 28, 2020 at 0:11
  • $\begingroup$ Very nice. I agree that the Table variant is the most semantically appealing option but the others worked equally well. $\endgroup$
    – mf67
    Jun 28, 2020 at 0:30

1 Answer 1

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Description

In essence, the solution below employs a pure function. The {#, 2#} defines the form of a sub-list structure where # is a slot. We then use a map /@ to take each element from the list {-3, 0, 4, 5} and plug it into the slot to generate the desired output.

Input

{#, 2 #} & /@ {-3, 0, 4, 5}

Output

{{-3, -6}, {0, 0}, {4, 8}, {5, 10}}

Reference

Pure Functions Map Slot

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    $\begingroup$ This is, in addition to C.E.'s suggestions above is also a very 'neat' syntax, with the slight modification of {#, y[#]} & /@ x $\endgroup$
    – mf67
    Jun 28, 2020 at 0:29

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