Answer
a. shift $ f(x)$ to the right 5 units.
b. compress horizontally by a factor of 4.
c. reflect about the y-axis and compress horizontally by a factor of 3.
d. compress horizontally by a factor of 2 and shift left 1/2 unit.
e. Stretch horizontally by a factor of 3 and shift down 4 units.
f. Reflect around x-axis, stretch vertically by a factor of 3, and shift up 1/4 unit.
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 $y-axis$
