# How do you plot a function on a cartesian plane?

Apr 21, 2018

There is a procedure to graph a function.

#### Explanation:

• Define the domain and codomain

• Find the intersection between function and x-axes:
solve $f \left(x\right) = 0$

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