#### Answer

a) $y = f(x) + 3$
b) $y = f(x)-3$
c) $y = f(x-3)$
d) $y = f(x+3)$
e) $y = -f(x)$
f) $y = f(-x)$
g) $y = 3f(x)$
h) $y = f(\frac{1}{3}x)$

#### Work Step by Step

a) You add 3 to the end of the function to shift it 3 units upwards
$y = f(x) + 3$
b) You subtract 3 from the end of the function to shift it 3 units downwards.
$y = f(x)-3$
c) You subtract 3 from the x within the function to shift the function 3 units to the right.
$y = f(x-3)$
d) You add 3 to the x within the function to shift the function 3 units to the left.
$y = f(x+3)$
e) You multiply the entire function to reflect it over the x-axis.
$y = -f(x)$
f) You multiply the x within the function to reflect it over the y-axis.
$y = f(-x)$
g) You multiply the entire function by 3 to vertically stretch it by 3.
$y = 3f(x)$
h) You multiply the x within the function by $\frac{1}{3}$ to horizontally stretch it by 3.
$y = f(\frac{1}{3}x)$