Question

How do you plot a function on a cartesian plane?

Answer 1

There is a procedure to graph a function.

Explanation:

• Define the domain and codomain

• Find the intersection between function and x-axes:
  solve `f(x)=0`

• Calculate the first derivative and its intersection with x-axes:
  `f'(x)=0`. This points are called extrema, geometrically represent the points where the tangent of the function is horizontal. This mean that the function reach its minimum or maximum or stationary points.

• Calculate the second derivative and its intersection with x-axes:
  `f''(x)=0`. This points (inflection point) are points on a curve at which the curve changes from being concave to convex or vice versa.
  if `f''(x)>0` the function is convex (is smiling)
  if `f''(x)<0` the function is concave (is sad)

Some typical example of domain.