For pre-calculus 12, is there a need for students to master the ability of graphing quartic or quintic functions without using graphing calculator?
I think it depends on how the functions are presented and how complicated they are. If they are given in factored form, then it's useful to be able to graph them. If they are not given in factored form it would be difficult or even impossible (in the case of some 5th degree polynomials) to find the exact values of the x-intercepts.
I have never used a graphing calculator in my life and I never needed it. So unless your teacher specifically told you that you need one for class, I wouldn't bother.