How is a graph of a function f(x) produced?

Question

Is every point of the graph evaluated numerically then graphed or are interpolations used?

I would really appreciate getting comments and answers to a question I have been asking myself for while and for which I couldn't find an answer.

Answer 1

When graphing a continuous function or curve that follows a particular formula you will need to use some form of interpolation to "fill in" the values between the ones you explicitly evaluate.

There are a number of ways to do this but two common ones are:

1. Linear Interpolation -- fit a line segment between adjacent points.
2. Splines -- generalizes interpolation to nonlinear interpolants (also called spline interpolation)

You can try these two out in Excel -- it uses both linear and "smooth" interpolations.