Practice problem

Piecewise Linear Functions

Train on tracks — Image by 12019 via Pixabay (CC0)

A train is traveling a total of $86$ miles today. The train travels $28$ miles in the first $14$ minutes of the trip. The train then slows down due to weather conditions. It goes another $18$ miles in $36$ minutes. The train then runs into a mechanical problem and stops for $10$ minutes. Once the problem is fixed, the train finishes the trip with another $40$ miles in $40$ minutes. Graph the piecewise function. What are the equations for the piecewise that result from that graph of the train trip?

Choose one answer

f(x)=\begin{cases} 2x&0\le{x}<14\\ \frac{1}{2}x&14\le{x}<50\\ 46&50\le{x}<60\\ x-14&60\le{x}<100 \end{cases}

f(x)=\begin{cases} 2x&0\le{x}<28\\ \frac{1}{2}x&28\le{x}<46\\ 46&46\le{x}<46\\ x-14&46\le{x}<86 \end{cases}

f(x)=\begin{cases} 2x&0\le{x}<14\\ \frac{1}{2}x+21&14\le{x}<50\\ 46&50\le{x}<60\\ x-14&60\le{x}<100 \end{cases}

f(x)=\begin{cases} x+28&0\le{x}<14\\ x+18&14\le{x}<50\\ 0&50\le{x}<60\\ x+40&60\le{x}<100 \end{cases}