Use plot
(in tikz
package) to draw functions in $\mathrm{\LaTeX}$.
\usepackage{tikz,amsmath}
The example below generates this graph.
\begin{tikzpicture}[scale=0.5] \draw[->] (0,0) -- (8,0) node[right] {$x$}; \draw[->] (0,0) -- (0,10) node[above] {$f(x)$}; \draw (1.5,0) -- (1.5,0.1) node[below] {$\frac{3}{2}$}; \draw (2.25,0) -- (2.25,0.1) node[below] {$\frac{5}{2}$}; \draw[dotted] (3,9) -- (3,0) node[below] {$3$}; \draw [domain=0:3] plot (\x,{4/3 * \x*\x*\x - 8*\x*\x+15*\x}) node[right] {$\frac{4}{3}x^3-8x^2+15x$}; \draw [domain=3:6] plot (\x,{9*exp(3-\x)}) node[right] {$9e^{3-x}$}; \end{tikzpicture}
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