By extrapolating we estimate a value outside the data domain, while an interpolation is an estimation of value inside the data domain.
See solution.
Practice makes perfect
Let's start by reviewing the concepts of interpolation and extrapolation. When we are given a set of data points x_0, x_1, ..., x_n, we can approximate a curve through and beyond them. This allows us to predict the function's value for other x-values. We can do this in two ways.
Extrapolating: This is when we predict the function's value for x values beyond the known values outside the domain of the data set — this is when xx_n.
Interpolating: This is when we predict the function's value for x values in between the known values — this is when x_0
Interpolating is a more precise estimation, since the value we look for lies inside the domain of the data set, where we have an idea of the function's behavior. Outside this domain we do not know if the function's behavior changes, and furthermore, the prediction gets worse as we move far from the data set we used for the approximation.
