Shattering and growth function

1. Which labelings can a class realize on n points xโ‚ < โ€ฆ < xโ‚™ of the line?

n =

2. The growth function N(๐“•, n), 2โฟ and the Sauer-Shelah bound

3. Exam training: is this a valid growth function?

values of N(๐“•, n) for n = 1, 2, 3, โ€ฆ:
These are necessary conditions. A row that passes them is consistent with everything the lecture says about growth functions.