Notice that for each increase in 4 units of the variable x, the function f(x) increases by 5 units.
Then:
[tex]\begin{gathered} f(-2)+5=f(-2+4) \\ \\ \Rightarrow f(-2)+5=f(2) \\ \\ \Rightarrow f(-2)=f(2)-5 \\ \\ \Rightarrow f(-2)=2-5 \\ \\ \therefore\quad f(-2)=-3 \end{gathered}[/tex]
Therefore, k=-3.
