3. Boccioni's futurist work ``Unique Forms of Continuity in Space'' from 1913, featured on the 20-cent coin, depicts a man advancing rapidly through space. A part of the profile highlighted in the figure, in an appropriate coordinate system, can be approximated by the function $$f ( x ) = \left\{ \begin{array} { l r }
- 4 x ^ { 2 } - 8 x , & - 1 \leq x \leq 0 \\
1 + \tan \left( x + \frac { 3 } { 4 } \pi \right) , & 0 < x \leq 2
\end{array} \right.$$ Sketch the graph of $f$, after analyzing its continuity and differentiability on the interval $[ - 1 ; 2 ]$. [Figure]
3. Boccioni's futurist work ``Unique Forms of Continuity in Space'' from 1913, featured on the 20-cent coin, depicts a man advancing rapidly through space. A part of the profile highlighted in the figure, in an appropriate coordinate system, can be approximated by the function
$$f ( x ) = \left\{ \begin{array} { l r }
- 4 x ^ { 2 } - 8 x , & - 1 \leq x \leq 0 \\
1 + \tan \left( x + \frac { 3 } { 4 } \pi \right) , & 0 < x \leq 2
\end{array} \right.$$
Sketch the graph of $f$, after analyzing its continuity and differentiability on the interval $[ - 1 ; 2 ]$.\\
\includegraphics[max width=\textwidth, alt={}, center]{2f895d94-69f9-4afb-b50c-7dcb321c9ec9-3_754_654_1069_1254}