Piecewise functions
===================

#. Write the function :py:func:`fun_mat_1` that takes an ``x`` value
   (float), and returns ``f(x)`` (float).

   .. math::
      
      f(x) = 
      \begin{cases}
      \frac{5x-1}{\sqrt{\lvert x-1 \rvert}} & x<=-1 \\
      2^{x} & x>-1
      \end{cases}

   Save this function into a file named ``fun_mat_1.py``. See the
   following examples:
   
   .. literalinclude:: fun_mat_1.txt
      :language: python3
      :lines: 3-

   .. note::
      More tests are provided in the
      :download:`fun_mat_1.txt<fun_mat_1.txt>` file

#. Write the function :py:func:`fun_mat_2` that takes two values ``x``
   and ``y`` (float), and returns ``g(x, y)`` (float).

   .. math::
      
      g(x,y) = 
      \begin{cases} 
        \frac{x^2-y^2}{e^{x+y}-1}  & x>-y, \\
        2^x                         & x=-y, \\
        \frac{\sin (x^2-y^2)}{x+y} & x<-y.
      \end{cases}

   Save this function into a file named ``fun_mat_2.py``. See the
   following examples:
   
   .. literalinclude:: fun_mat_2.txt
      :language: python3
      :lines: 3-

   .. note::
      More tests are provided in the
      :download:`fun_mat_2.txt<fun_mat_2.txt>` file

#. Write the function :py:func:`fun_mat_3` that takes two values ``x``
   and ``y`` (float), and returns ``h(x, y)`` (float).

   .. math::

      h(x,y) = 
      \begin{cases} 
      x^2+y, & \mbox{si } x>=1\\
      sin(x), & \mbox{si } 0<x<1\\
      y*cos(x), & \mbox{si } x<=0
      \end{cases}

   Save this function into a file named ``fun_mat_3.py``. See the
   following examples:
   
   .. literalinclude:: fun_mat_3.txt
      :language: python3
      :lines: 3-

   .. note::
      More tests are provided in the
      :download:`fun_mat_3.txt<fun_mat_3.txt>` file

.. rubric:: Solution

Solutions are provided in files :download:`fun_mat_1.py
<solutions/fun_mat_1.py>`, :download:`fun_mat_2.py
<solutions/fun_mat_2.py>` and :download:`fun_mat_3.py
<solutions/fun_mat_3.py>`