How to calculate growth function for a threshold function I'm working on a homework problem but don't fully understand it. The problem and solution:



I don't understand the definition of the threshold function. 

Does it mean to pick one feature and classify the point based on that one feature? 

It's the only way I can think of to explain the solution, $N$ ways to pick a feature, for each feature there are $m+1$ ways to select the threshold.
Yes, your interpretation is correct. 

Each member of $H$ is one such function, they are parametrized by $i$, the feature selected and $\theta$, the chosen threshold. Different $\theta$ might corresponds to the same function but effectively there are only $m+1$ such function for each $i$. Hence, the set $H$ consists of at most $(m+1)N$ elements.