Why do non-linear functions have to be in V or U shape, why can't it just be one line?

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The title says it all really, I just don't get why you can't just use one line.

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If you mean a "straight line", then it's because a function with such a graph is always linear (so, not non-linear).

Linear functions are precisely those whose graphs are (nonvertical) lines.

I'm assuming we're talking about real-valued functions of a single real variable (functions $\mathbb R\to\mathbb R$).