# Converting a graph into a function

Is is possible to convert this graph into an function of t(time), if what are the appropriate steps to do this? Any help point in the general direction will be greatly appreciated! Thanks in advance. EDIT: Sorry about not being clear in the question, in the end a function q(t) that represents the graph is what I'm looking for! Thanks again

• Piecewise function – daOnlyBG Nov 14 '14 at 7:52
• I think it is not clear what do you want. – mcihak Nov 14 '14 at 7:53

## 1 Answer

$$q(t) = \cases{7.5t & \text{ , if } 0 \le t \le 2\\ 15 & \text{ , if } 2 < t < 4 \\ 15-5(t-4) &\text{ , if } 4 \le t \le 7 \\ 0 &\text{ , otherwise}}$$

You get this by considering the intervals $(-\infty, 0), [0,2], (2,4), [4,7]$ and $(7,\infty)$ individually.

• Is is possible to have it all as one function or must you split it up into multiple? Thanks for the help also! – Exodical Nov 14 '14 at 8:10
• This is ONE function. We can represent it in many different ways, tho. The piecewise definition, I stated, is a good (and very common) way to think about such functions, as it is easy to both write down and read. – Stefan Mesken Nov 14 '14 at 8:16