Answer
(a) $-12, -3$
(b) $ -5, 4$
(c) $ -8, 1$
(d) $ -1, 8$
Work Step by Step
The $x$-intercepts of $y=f(x)$ are $-8$ and $1$.
(a) $y=f(x+4)$ shifts the curve $y=f(x)$ four units to the left. Thus the $x$-intercepts of $y=f(x+4)$ are equal to the intercepts of $y=f(x)$ moved $4$ units to the left.
Therefore, the $x$-intercepts are:
$x=-8-4=-12$
and
$x=1-4=-3$
(b) $y=f(x-3)$ shifts the curve $y=f(x)$ three units to the right. Thus the $x$-intercepts of $y=f(x-3)$ are equal to the $x$-intercepts of $y-(x)$ shifted $3$ units to the right.
Therefore, the $x$-intercepts are:
$x=-8+3=-5$
and
$x=1+3=4$
(c) $y=2f(x)$ stretches the curve $y=f(x)$ vertically by a factor of $2$. This does not affect the $x$-intercepts therefore the $x$-intercepts of $y=2f(x)$ are also $-8$ and $1$.
(d) $y=f(-x)$ reflects the curve $y=f(x)$ about the $y$-axis, thus the its $x$-intercepts are the additive inverses of the $x$-intercepts of $y=f(x)$.
Therefore, the $x$-intercepts of $y=f(-x)$ are $x=8$ and $-1$
