Answer
(a) $x=-7$ and $x=1$;
(b) $x=-3$ and $x=5$;
(c) $x=-5$ and $x=3$;
(d) $x=5$ and $x=-3$;
Work Step by Step
Given the x-intercepts $x=-5$ and $x=3$ of $y=f(x)$, we have:
(a) For $y=f(x+2)$, shift the x-coordinates 2 units to the left, thus new x-intercepts $x=-7$ and $x=1$;
(b) For $y=f(x-2)$, shift the x-coordinates 2 units to the right, thus new x-intercepts $x=-3$ and $x=5$;
(c) For $y=4f(x)$, stretch vertically by a factor of 4, thus new x-intercepts $x=-5$ and $x=3$;
(d) For $y=f(-x)$, reflect across the y-axis, thus new x-intercepts $x=5$ and $x=-3$;
