Answer
(a) $(-3,3)$;
(b) $(4,10)$;
(c) decreasing interval $(-1,5)$;
(d) decreasing interval $(-5,1)$.
Work Step by Step
Given an increasing interval $(-1,5)$ of $y=f(x)$, we have:
(a) For $y=f(x+2)$, shift the x-coordinates 2 units to the left, thus new increasing interval $(-3,3)$;
(b) For $y=f(x-5)$, shift the x-coordinates 5 units to the right, thus new increasing interval $(4,10)$;
(c) For $y=-f(x)$, reflect across the x-axis, thus we have a new decreasing interval $(-1,5)$;
(d) For $y=f(-x)$, reflect across the y-axis, thus we have a new decreasing interval $(-5,1)$.
