Originally Posted by

**SlipEternal** I can see why you are stumped. While HallsofIvy is inferring a relationship between the three lines and the piecewise linear function, the problem does not make this relationship apparent. **Is it saying that on the interval $[1,2]$, the function satisfies the equation $y=ax+b$?** Then on the interval $[2,3]$, the function satisfies the equation $y=cx+d$, and finally on the interval $[3,4]$, the function satisfies the equation $y=ex+f$? Because that is not what the problem states as it is written. I, personally, would say that this is not a problem that is possible to solve, but here goes:

$f(x) = \begin{cases}a+b & x \le 1 \\ ax+b & 1\le x \le 2 \\ cx+d & 2 \le x \le 3 \\ ex+f & 3 \le x \le 4 \\ 4e+f & 4 \le x\end{cases}$

That is a possibility. Now, write up five more possible piecewise linear functions (by changing the initial line or the last line).