Polynomial curve sketching on blender

Question

I know that blender is able to draw mathematics curves using function, example:

How to draw a flat ellipse surface in Blender with the following known dimensions?

Is there any code or method to insert a function $f(x)$ and get the curve?

How to limit the points of the curve as in the example in red?

Above, an ellipse is drawn in blender using the Bezier curve, through code and mathematical equations, to exemplify this question.

Answer 1

Try this script. Notice that your $f(x)$ function is in the get_graph_y definition which accepts an x value input in the range $2-8$ and computes its corresponding y value from the function. You can change the range and the function to anything as long as its of the form $y=y(x)$ and the script will plot the graph.

import bpy

def get_object(name):
    objects = bpy.context.scene.objects
    if name in objects:
        return objects[name]
    m = bpy.data.meshes.new(name + "-mesh")
    o = bpy.data.objects.new(name, m)
    #o.modifiers.new(name, 'SKIN')
    bpy.context.collection.objects.link(o)
    return o 

def get_range(start, end, step = 2):
    return [v * 0.1 for v in range(start * 10, end * 10, step)]

def get_graph_y(x):
    return 0*x**3 - 0.09*x**2 + 0.42*x + 0.49

def draw_graph():
    verts = []

    for px in get_range(2, 8):
        py = get_graph_y(px)
        pz = 0
        verts.append([px, py, pz])

    edges = []
    for i in range(len(verts)-1):
        edges.append((i, i+1))

    o = get_object("graph")
    m = o.data
    m.clear_geometry()
    m.from_pydata(verts, edges, ())

draw_graph()

Take note that you can also easily plot this using Geometry Nodes. I'll update my answer with a GN solution later.