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What kind of function is represented by this graph?

I've created an example for this question:

Graph

For every $x$ I increase $y$ by $1$. But for every fourth $x$-value I increase $y$ by $2$ instead of $1$. I wonder how I could describe this by a function.

Kntlii
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  • Are the only valid values for $x, y$ integers? Is the domain of the function (on which the function is defined) $x\in [0, 8]$? You need to fill such details. – amWhy Jul 21 '17 at 22:15
  • You’ve already described this by a function, but I suppose that you’re looking for some closed-form formula. – amd Jul 21 '17 at 22:18
  • Until this asker cares enough to comment and edit his/her post to clarify their post and to answer the questions folks have, I think users who try to "guess" what they mean and answer upon their interpretation, before the OP clarifies should not be rewarded. You really need to specify to in which set $x, y$ are elements. The connecting the points given by $(x, y), x, y\in \mathbb Z$ isn't valid, unless $x, y$ can only be integers. – amWhy Jul 21 '17 at 22:36

2 Answers2

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$y(x) = x + \lfloor x/4 \rfloor$ for $x \in \mathbb{Z}$.

David G. Stork
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It is a piecewise function.

$$1\le x\le 3 \implies f (x)=x $$

$$4\le x\le 7 \implies f (x)=x+1$$ $$f (8)=10$$

hamam_Abdallah
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    Ummm... so what about $x = 93.7$, for instance? – David G. Stork Jul 21 '17 at 22:05
  • @DavidG.Stork Our function is defined for $x\in [1,8] $ only. For x=93.7, you can take f (x)=-73.99999999999999. – hamam_Abdallah Jul 21 '17 at 22:12
  • @Salahamam_Fatima We don't know that, that it's range is $x \in [0, 8].$ You treat $x$ as though $x \in \mathbb R$, (rather, you never specify your domain). What's the fourth value of $x \in [0, 8] \subset \mathbb R$. – amWhy Jul 21 '17 at 22:22
  • Hmm... I don't remember saying that. Oh, indeed I sleep! I love my sleep-time. But when I'm engaged in any activity, my brain "never sleeps", indeed, every moment in which I am physically awake, my brain is awake and focused!. – amWhy Jul 21 '17 at 22:30