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)=
{25x - 1500 if 0 < x < 40
0 if 40 <= x <= 65
25x - 1500 if x > 65}

Explanation:

Step1: Define function parts

For \(0 < x < 40\), fine is based on under - minimum speed. For \(40\leq x\leq65\), no fine (\(F(x)=0\)). For \(x > 65\), fine is based on over - maximum speed.

Step2: Write piece - wise function

\[F(x)=

$$\begin{cases}25x - 1500, &\text{if }x>65\\0, &\text{if }40\leq x\leq65\\25x - 1500, &\text{if }0 < x < 40\end{cases}$$

\]

Answer:

\[F(x)=

$$\begin{cases}25x - 1500, &\text{if }x>65\\0, &\text{if }40\leq x\leq65\\25x - 1500, &\text{if }0 < x < 40\end{cases}$$

\]