What are basis functions does an approximant vx that is, Basic Computer Science

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What are basis functions does an approximant vx that is

1. Distinguish between the terms data fitting, interpolation, and polynomial interpolation.

2. Distinguish between (discrete) data fitting and approximating a given function.

3. What are basis functions? Does an approximant v(x) that is written as a linear combination of basis functions have to be linear in x?

4. An interpolating polynomial is unique regardless of the choice of the basis. Explain why

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