Question

in a certain state the maximum speed permitted on freeways is 65 mi/h, and the minimum is 40 mi/h. the fine f for violating these limits is $25 for every mile above the maximum or below the minimum. (a) complete the expressions in the following piece - wise defined function, where x is the speed (in mi/h) at which you are driving. f(x)=\\(\

$$\begin{cases} & \\text{if }0 < x < 40 \\\\ 0 & \\text{if }40\\leq x\\leq65 \\\\ & \\text{if }x > 65 \\end{cases}$$

$

Explanation:

Step1: Analyze speed ranges

When \(0 < x < 40\), \(F(x)=25(40 - x)\) (fine for being below min). When \(40\leq x\leq65\), \(F(x) = 0\) (within limits). When \(x>65\), \(F(x)=25(x - 65)\) (fine for being above max).

Answer:

\(F(x)=

$$\begin{cases}25(40 - x),&0 < x < 40\\0,&40\leq x\leq65\\25(x - 65),&x>65\end{cases}$$

\)