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.

• Will it possible for you to share the source of this problem? Nov 5 '17 at 2:39
• Hmm...I believe it's okay since it's an old homework, open on the internet and everyone can just google it. Here you go: cs.nyu.edu/~mohri/ml14/hw2.pdf Nov 5 '17 at 14:39

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.