# How do you graph y=1/3 cosx?

You are modifing a function by scalar multiplication, i.e. you're going from $f \left(x\right)$ to $\lambda f \left(x\right)$, being $\lambda$ some real number.
This kind of changing only affects the amplitude of the function. In fact, if $\cos \left(x\right)$ ranges from $- 1$ to $1$, then $\frac{1}{3} \cos \left(x\right)$ will range from $- \frac{1}{3}$ to $\frac{1}{3}$.
You can see that all the rest remains untouched, if $f \left({x}_{0}\right) = 0$ for some ${x}_{0}$, then also $\lambda f \left({x}_{0}\right)$ will be zero.
Moreover, also the derivatives are in the same relation, since $\left(\lambda f \left(x\right)\right) ' = \lambda f ' \left(x\right)$, so $\lambda f \left(x\right)$ is growing if and only if $f \left(x\right)$ was growing too, and vice versa.
Of course, all I wrote applies when $\lambda$ is positive, otherwise you can switch $\lambda$ to $- \lambda$ and repeat everything about $- f \left(x\right)$.