Any 'nice' function can be approximated near a point by a polynomial — a Taylor series. The more terms you add, the better the fit.
Taylor series at x = 0
f(x) ≈ f(0) + f'(0)x + f''(0)x²/2! + f'''(0)x³/3! + …
Try it
Approximate eˣ near 0
1 + x + x²/2 + x³/6 + x⁴/24 + … (works for any x; converges everywhere)