Answer
(a) We plot $f(x)+3$
(b) We plot $f(x)-3$
(c) We plot $f(x-3)$
(d) We plot $f(x+3)$
(e) We plot $-f(x)$
(f) We plot $f(-x)$
(g) We plot $3f(x)$
(h) We plot $\frac{1}{3}f(x)$
Work Step by Step
(a) We plot $f(x)+3$
This is because every value on the vertical axis will increase by $3$.
(b) We plot $f(x)-3$
This is because every value on the vertical axis will decrease by $3$
(c) We plot $f(x-3)$
This is because everything that "happens" to $f(x)$ will happen to $f(x-3)$ three units of $x$ to the right.
(d) We plot $f(x+3)$
This is because everything that "happens" to $f(x)$ will happen to $f(x+3)$ three units of $x$ to the left.
(e) We plot $-f(x)$
This is because the values of the function that are on the $y$ axis change the sign.
(f) We plot $f(-x)$
This is because everything that happened to the function on the one side of $y$ axis (let's say when $x$ is positive) now will happen on the other side because we take $-x$ as the argument.
(g) We plot $3f(x)$
Every value of the function will be $3$ times bigger so it will appear stretched vertically.
(h) We plot $\frac{1}{3}f(x)$
Every value of the function will be $3$ times smaller so it will appear shrunk vertically.
