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I'm wondering if is it possible to plot a graph of a function with arbitrary constants.

Here's an example to make things clearer. If I have a function $$f(x) = \cos(bx) + bx$$ Can I plot this f(x) without giving a specific value for b?

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  • $\begingroup$ With Manipulate you can set a range for b and see how it affects the plot. $\endgroup$ Commented Nov 18, 2022 at 22:24
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    $\begingroup$ Manipulate[Plot[Cos[b x] + b x, {x, 0, 2Pi}], {b, 0, 3}] $\endgroup$ Commented Nov 18, 2022 at 22:25
  • $\begingroup$ Can I plot this f(x) without giving a specific value for b? The short answer is "no". Please lookup FunctionDomain and FunctionRange as those may help you in certain instances to plot a region of interest. $\endgroup$ Commented Nov 19, 2022 at 3:39
  • $\begingroup$ Do you want to draw all of the curves for -2<=b<=2? $\endgroup$ Commented Nov 19, 2022 at 3:46
  • $\begingroup$ If you use free form syntax with Ctrl + = then type plot Cos[xb]+xb you will get a 3 D plot if you want that. It might be easier to visualize the curve for different b with the suggestion above to use Manipulate or the answer below. $\endgroup$ Commented Nov 19, 2022 at 7:45

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Different values of $b$ correspond to different scales of the $x$-axis (I will assume $b>0$). Therefore, one could use a plot of this kind:

enter image description here

Code:

With[{xs=Range[-3*Pi,3*Pi,Pi]},
 Plot[Cos[x]+x,{x,Min[xs],Max[xs]},
  Ticks->{{xs,xs/"b"}//Transpose,Automatic}]]
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