How to draw the graph of $8x^3 -6x+1=0$?

Question

How to draw the graph of $8x^3 -6x+1=0$?

Any generalization of a graph of polynomials of degree 3 is helpful.

Answer 1

A good method I use to plot graphs:

A) Domain

B) Intercepts $x,y=0?$

C) Symmetry/Periodicity:

Symmetry: If $f(-x)=f(x)$ on the domain then it is EVEN (symmetric about y axis).

Or $f(-x)=-f(x)$ on domain then it is ODD (symmetric about the origin).

Can be neither odd or even.

Periodicity: Where $f(x+p)=f(x)$ where $p$ is a positive constant.

D) Asymptotes (horizontal/vertical)

E) Intervals of increase or decrease ($f'(x)$)

F) Local Min/Max or Inflection ($f'(x)=0$)

G) Concavity ($f''(x)$)