Answer
(a) graph 2
(b) graph 3
(c) graph 1
(d) graph 4
Work Step by Step
(a) $y=\displaystyle \frac{1}{3}f(x)$ is $f(x)$ compressed vertically by $\frac{1}{3}$, so this matches graph 2.
(b) $y=-f(x+4)$ is $f(x)$ flipped around the $x$-axis and moved left 4 units, so this matches graph 3.
(c) $y=f(x-5)+3$ is $f(x)$ moved right 5 units and up 3 units, so this matches graph 1.
(d) $y=f(-x)$ is $f(x)$ reflected around the $y$-axis, so this matches graph 4.
