Strictly increasing function transformation I have utility function given by:

$U(x_1, x_2) =
  \begin{cases}
                                   x_1+x_2 &amp; \text{if $x_1+x_2&lt;6$} \\
                                   6 &amp; \text{if $6\leq x_1+x_2\leq10$} \\
                                   x_1 + x_2 &amp; \text{if $x_1+x_2&gt;10$}
  \end{cases}$

If I transform this to this:

$F(U(x_1, x_2)) =
  \begin{cases}
                                   U(x_1, x_2)+4 &amp; \text{if $U(x_1, x_2)&lt;6$} \\
                                   10 &amp; \text{if $U(x_1, x_2)=6$} \\
                                   U(x_1, x_2) &amp; \text{if $U(x_1, x_2)&gt;10$}
  \end{cases}$

Is it strictly increasing function transformation?

Thanks guys
This is a strictly increasing monotonic transformation simply because the preferences in the previous function are the same in the transformed function as well.