th $n$ components, and $\vec y$ is a vector in
      $\RR^m$ with $m$ components.
    </div>

    For the function $f(x,y)=z$, we can write $f$ in the vector
    notation $\vec y=\vec f(\vec x)$ if we let $\vec x=(x,y)$ and
    $\vec y=(z)$. Notice that $\vec x$ is a vector of inputs, and
    $\vec y$ is a vector of outputs. For each of the functions
    below, state what $\vec x$ and $\vec y$ should be so that the
    function can be written in the form $\vec y = \vec f (\vec x)$.

    <ol>
      <li>$f(x,