Answer
a. $ g(x-3)+\frac{1}{2}$
b. $ g(x+\frac{2}{3})-2$
c. $ g(-x)$
d. $-g(x)$
e. $5g(x)$
f. $ g(5x)$
Work Step by Step
Recall the general rules for graph transformations (here $a,b,c,d$ are integers):
$(x+c)\implies$ shift left by $c$
$(x-c)\implies$ shift right by $c$
$f(x)+d\implies$ shift up by $d$
$f(x)-d\implies$ shift down by $d$
$af(x)$ stretch graph by $a$ vertically
$\dfrac{1}{a}f(x)$ shrink graph by $a$ vertically
$f(bx)$ shrink graph by $b$ horizontally
$f(\dfrac{x}{b})$ stretch graph by $b$ horizontally
$-f(x)$ reflect around $x-axis$
$f(-x)$ reflect around $y-axis$
