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) $y = \frac{1}{3}f(x)$
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 function by $\frac{1}{3}$ to vertically shrink it by $3$.
$y = \frac{1}{3}f(x)$
