Prove or give a counter example.

If Dom $($f$)=$R and f is increasing on the intervals $-2,-1$ and $1,2,$

then f is increasing on $-2,2.$

Answer:

The function f given by

f$($x$)=\{($x$+1$ if xx if $0=1)$:$\}$

is one counterexample. Another is f$($x$)=($x$+1)($x$-1)^(2).$