Is there cases where interpolation is impossible? I just learned interpolation and have been looking through it. 

It seems like for every data set, interpolation is possible -- is this true? Is there any cases it is not possible to use interpolation?

Any hints or help on this question will greatly help!!!
Consider the data set $x_0 = 0$, $y_0 = 0$, $x_1 = 0$, $y_1 = 1$. No function can serve as the interpolation here.
Do you know the tangent function?

You have $\tan 0 = 0$ and $\tan \pi = 0$. Dare to interpolate for $\frac\pi 2$...?