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I am plotting a non-linear function -2/3 x^ 3 + x^2-3x+4/3 in the interval [0,1/2], I tried to change the scales to make it look less linear but still looks like a straight line. Any suggestions?

\usepackage{tikz}
\begin{figure}
\begin{tikzpicture}[xscale=5,yscale=3,domain=0:1,step=.01];
\draw[<->] (0,1.5)--(0,-.3);
\draw[<->] (-.3,0)--(1,0);
\draw[] (1,0) node[right]{\small $x$};
\draw[color=blue]   plot[samples=200] (\x,{ifthenelse(\x <.5,-(2/3)*\x^3+\x^2-3*\x+4/3,(2/3)*\x^3-\x^2+3*\x-4/3))}) node[right] {\small{$b(x)$}};
\draw[color=red] (-.2,0.635) node[right]{$\beta$};
\draw[color=red] (0,0.635)--(1,0.635);
\draw[color=red,dotted,thick](.25,-.3)--(.25,0.635);
\draw[color=red,dotted,thick](.75,-.3)--(.75,0.635);
\draw[color=red](.25,-.3)node[below]{\footnotesize{$\phi_1(\beta)$}};
\draw[color=red](.75,-.3)node[below]{\footnotesize{$\phi_2(\beta)$}};
\end{tikzpicture} 
\end{figure}
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  • Welcome to tex.stackexchange.com. I edited your question by indenting your code by 4 spaces, so that it gets formatted correctly. – yori Apr 17 '14 at 15:40
  • @Yori: thanks! I went to other posts to see why my code was muddled but by the time I started editing it, you had already fixed it. – Sergio Parreiras Apr 17 '14 at 15:41
  • 1
    Also, we usually ask for a minimum working example (MWE) which highlights the core of the problem. Your example (a) does not compile and (b) seems to have a lot of code that is irrelevant for the question. You have a better chance of getting a good answer by removing the irrelevant code. – yori Apr 17 '14 at 15:43
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PSTricks can help to analyze the graph.

Because in the given interval 0 <= x <= 1/2 the function f(x)=(-2*x^3+3*x^2-9*x+4)/3 is almost identical to the line g(x)=(-8*x+4)/3 passing (0,f(0)) and (1/2,f(1/2)) as shown in the following figure.

\documentclass[pstricks,border=24pt]{standalone}
\usepackage{pst-plot}

\def\f{(-2*x^3+3*x^2-9*x+4)/3}
\def\g{(-8*x+4)/3}
\begin{document}
\begin{pspicture}[algebraic](1,1.5)
    \psaxes{->}(0,0)(0,0)(.75,1.25)[$x$,0][$y$,90]
    \psset{linewidth=.4pt}
    \psplot[linecolor=red]{0}{.5}{\f}
    \psplot[linecolor=blue]{0}{.5}{\g}
    \psplot[linecolor=green]{0}{.5}{abs(\f-\g)}
\end{pspicture}
\end{document}

enter image description here

  • The red is the graph of f(x)=(-2*x^3+3*x^2-9*x+4)/3.
  • The blue is the graph of g(x)=(-8*x+4)/3.
  • The green is the graph of |f(x)-g(x)|.

That is why scaling will not help.

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2

I would say you can't because your interval is too small.

See how the plot looks in wolfram alpha using small axis limits.

https://www.wolframalpha.com/input/?i=-2%2F3+x%5E+3+%2B+x%5E2-3x%2B4%2F3+on+interval+0+to+0.5

Image generated from wolframalpha

enter image description here

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