Answer
(a) $-7$ and $1$
(b) $-3$ and $5$
(c) $-5$ and $3$
(d) $-3$ and $5$
Work Step by Step
The $x$-intercepts of $y=f(x)$ are $x=-5$ and $x=3$.
(a) $y=f(x+2)$ involves a $2$-unit shift to the left of $y=f(x)$. Thus, the new function's $x$-intercepts are equal to the intercepts of $y=f9x)$ shifted $2$ units to the left.
Thus, the $x-$intercepts of the new functions are:
$x=-5-2=-7$
and
$x=3-2=1$
(b) $y=f(x-2)$ shifts the curve $y=f9x)$ $2$ units to the right. Thus the new $x$-intercepts are:
$x=-5+2=-3$
and
$x=3+2=5$
(c) $y=4f(x)$ stretches the curve $y=f(x)$ vertically by a factor of $4$, which will not affect the $x$-intercepts. Thus, the $x$-intercepts are still $x=-5, 3$.
(d) $y=f(-x)$ reflects the curve $y=f(x)$ about the $y$-axis, thus the new $x$-intercepts are the additive inverses of the $x$-intercepts of $y=f(x)$. Hence, the $x$-intercepts are $x=5, -3$
