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POabout plotting process -- a further question about "A problem in Mathematica 8 with function declaration"
 

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  1. POabout plotting process -- a further question about "A problem in Mathematica 8 with function declaration"
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    <p>Related <a href="https://stackoverflow.com/questions/6046626/a-problem-in-mathematica-8-with-function-declaration">A problem in Mathematica 8 with function declaration</a></p> <pre><code>Clear["Global`*"] model = 4/Sqrt[3] - a1/(x + b1) - a2/(x + b2)^2 - a3/(x + b3)^4; fit = {a1 -&gt; 0.27, a2 -&gt; 0.335, a3 -&gt; -0.347, b1 -&gt; 4.29, b2 -&gt; 0.435, b3 -&gt; 0.712}; functionB1[x_] = model /. fit; functionB2[x_] := model /. fit; </code></pre> <p>The evaluation difference between functionB1 and functionB2 can be revealed by <code>Trace</code> command in mma, as below:</p> <pre><code>functionB1[Sqrt[0.2]] // Trace functionB2[Sqrt[0.2]] // Trace </code></pre> <p>I have no question about functionB1. <strong>what puzzles me is that</strong> because <code>functionB2[Sqrt[0.2]]</code> doesn't even gives a numeric result but gives a function of x <code>4/Sqrt[3] - 0.335/(0.435 + x)^2 + 0.347/(0.712 + x)^4 - 0.27/( 4.29 + x)</code>, and then how its plot <code>Plot[functionB2[Sqrt[x]], {x, 0, 1}]</code> is possible? </p> <p>I mean when you run <code>Plot[functionB2[Sqrt[x]], {x, 0, 1}]</code>, what happens inside mma is:</p> <p>x takes a number, say, 0.2, then 0.2 is finally passed to functionB2, but functionB2 gives a function, not a number. Then how is the following figure generated?</p> <p><img src="https://i.stack.imgur.com/Scrrn.gif" alt="enter image description here"></p> <p>And its trace result ( <code>Plot[functionB2[Sqrt[x]], {x, 0, 1}] // Trace</code> ) seems very unreadable. I wonder the clear plotting process of functionB2. Can anybody show it?</p> <p>thanks~ :)</p>
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    1. CO@FreashApple Allow me to welcome you to StackOverflow and remind three things we usually do here: 1) As you receive help, try to give it too **answering questions** in your area of expertise 2) [`Read the FAQs`](http://tinyurl.com/2vycnvr) 3) When you see good Q&A, vote them up by [`using the gray triangles`](http://i.imgur.com/kygEP.png), as the credibility of the system is based on the reputation that users gain by sharing their knowledge. Also remember to accept the answer that better solves your problem, if any, [`by pressing the checkmark sign`](http://tinyurl.com/4srwe2t)
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