I fed this inequality into Wolfram/Alpha:

Mod[-1 + 2^(1 - IntegerExponent[2 + 2 x, 2]) 3^ IntegerExponent[2 + 2 x, 2] (1 + x), 1 + 2 x] < 1 + 2 x,

and got this plot:

The uploads didn't format properly, so I just have the image. I copied the function for the plot and got:

Plot[{Mod[-1 + 2^(1 - IntegerExponent[2 + 2 x, 2]) 3^ IntegerExponent[2 + 2 x, 2] (1 + x), 1 + 2 x], 1 + 2 x}, {x, -5.01, 5.01}]

This doesn't work. So I have some questions:

Q1) How can I get Mathematica 9 to replicate the plot?

Q2) How can I determine the x-,y-axis ratio? (It looks like 1:2, but I want to be sure.)

Q3) If 1:2 is the case, what is there about the formula that would indicate that this is a good ratio?

• I have no idea what Wolfram|Alpha is trying to show you, since you're asking about an inequality in a single variable and whose solution would therefore be a subset of the x-axis rather than some graph in the plane. So Plot is not an appropriate function to try. Moreover,IntegerExponent expects an integer as first argument, and clearly that's not what you're giving it as x ranges over the interval you indicated. In fact, you'll generate IntegerExponent::int error messages if you try the evaluation. Commented Feb 2, 2014 at 17:19
• Further, you fed Wolfram|Alpha an inequality, whereas the Plot expression you then give is requesting a plot of a pair of two functions. Still you have the problem of the errors with IntegerExponent. Commented Feb 2, 2014 at 17:20
• @murray, the plot expression is from WA Commented Feb 2, 2014 at 17:46
• OK, I see now, in view of the answer from @belisarius: Wolfarm|Alpha converts your inequality into the pair of functions on its two sides, tries to plot that, and shows just the plot of the right-hand side -- because it cannot possibly plot the left-hand side due to the IntegerExponent domain problem. Commented Feb 2, 2014 at 17:59

Please see the comments by @Murray in your question. WolframAlpha is just plotting (1 + 2 x), as can be seen here: