Paste a table of x,y readings and ask for values in between. Linear interpolation rides the segments; the Lagrange polynomial threads every point at once and prints its expanded formula. Goes backwards too ā give it a y and it finds x ā and it says so out loud when you drift outside the data and start extrapolating.
One point per line as x, y. Duplicate x values are rejected ā a function can't have two answers.
Degree-8 Lagrange through equally spaced points oscillates wildly near the ends (Runge's phenomenon) ā that's the price of one smooth polynomial; cubic splines exist because of it. Use the linear answer outside the data range with suspicion.