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mod graph combinations

I got the right answer to this q, but looking back I don't really see why this logic is correct.
math.png
Initially, it made sense since each one of the 4 segments, can either be below the x axis or above it, which means 2 options for each of the 4, so 2^4 = 16.

But why cant each segment be both above and below it? I dont think theres anything in the q preventing this? i.e.

example.png

In this case there are 3 options for each segment (above/below the xaxis or both), so shouldn't the answer be 3^4 = 81?
Help greatly appreciated.
(edited 8 months ago)

Reply 1

Original post by mosaurlodon
I got the right answer to this q, but looking back I don't really see why this logic is correct.
math.png
Initially, it made sense since each one of the 4 segments, can either be below the x axis or above it, which means 2 options for each of the 4, so 2^4 = 16.
But why cant each segment be both above and below it? I dont think theres anything in the q preventing this? i.e.
example.png
In this case there are 3 options for each segment (above/below the xaxis or both), so shouldn't the answer be 3^4 = 81?
Help greatly appreciated.

f(x) is a function, so for each x, there is a single output. It could be argued that the question says curve rather than function, though ...

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