Answer
(a) $(-4,5)$;
(b) $(3,12)$;
(c) increasing interval $(-2,7)$;
(d) increasing interval $(-7,2)$.
Work Step by Step
Given a decreasing interval $(-2,7)$ of $y=f(x)$, we have:
(a) For $y=f(x+2)$, shift the x-coordinates 2 units to the left, thus new decreasing interval $(-4,5)$;
(b) For $y=f(x-5)$, shift the x-coordinates 5 units to the right, thus new decreasing interval $(3,12)$;
(c) For $y=-f(x)$, reflect across the x-axis, thus we have a new increasing interval $(-2,7)$;
(d) For $y=f(-x)$, reflect across the y-axis, thus we have a new increasing interval $(-7,2)$.
