Answer
$a.\quad (-4,5).$
$b.\quad (3,12)$
$c.\quad -f(x)$ decreases on $(-2,7)$
$d.\quad f(-x)$ decreases on $(-7,2)$
Work Step by Step
$a.$
The graph of f(x) is translated to the left by $2$ units, so the interval of increase is now
$(-2-2,7-2)=(-4,5)$
$b.$
The graph of f(x) is translated to the right by $5$ units, so the interval of increase is now
$(-2+5,7+5)=(3,12)$
$c.$
The graph of f(x) is reflected about the x-axis, so it now decreases where it used to increase.
$-f(x)$ decreases on $(-2,7)$
$d.$
The graph of f(x) is reflected about the y-axis, so it now decreases on an interval
corresponding to the one where it used to increase.
The borders of the interval were also reflected, so
$f(-x)$ decreases on $(-7,2)$