Starting AoPS’s Precalculus book this year

Since we stopped home schooling about 2 years ago I’ve mostly been doing projects with my kids rather than covering new content. This year I wanted to get back into content and have decided to do a slow walk through Art of Problem Solving’s Precalculus book with my older son.

Today this problem gave him a little trouble:

Find the domain and range of f(x) = 1 / (1 + \frac{1}{x})

We talked about the problem when he got home from school tonight. Here’s what he thought about the domain:

Next we talked about the range which is a more complicated problem (at least I think so anyway):

So, I’m happy that he was able walk through this explanation after school today. WE spent a while talking about it this morning and I was hoping that the ideas wouldn’t slip out of his mind during the day.

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