Answer
(a) $x=-12$ and $x=-3$;
(b) $x=-5$ and $x=4$;
(c) $x=-8$ and $x=1$;
(d) $x=8$ and $x=-1$.
Work Step by Step
Given the x-intercepts $x=-8$ and $x=1$ of $y=f(x)$, we have:
(a) For $y=f(x+4)$, shift the x-coordinates 4 units to the left, thus new x-intercepts $x=-12$ and $x=-3$;
(b) For $y=f(x-3)$, shift the x-coordinates 3 units to the right, thus new x-intercepts $x=-5$ and $x=4$;
(c) For $y=2f(x)$, stretch vertically by a factor of 2, thus new x-intercepts $x=-8$ and $x=1$;
(d) For $y=f(-x)$, reflect across the y-axis, thus new x-intercepts $x=8$ and $x=-1$.
