Answer
$a.\quad (-3,3).$
$b.\quad (4,10)$
$c.\quad -f(x)$ decreases on $(-1,5)$
$d.\quad f(-x)$ decreases on $(-5,1)$
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
$(-1-2,5-2)=(-3,3)$
$b.$
The graph of f(x) is translated to the right by $5$ units, so the interval of increase is now
$(-1+5,5+5)=(4,10)$
$c.$
The graph of f(x) is reflected about the x-axis, so it now decreases where it used to increase.
$-f(x)$ decreases on $(-1,5)$
$d.$
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 $(-5,1)$
