Question

1. modeling real life miami - dade county issues tickets for speeding as follows.

• no more than 9 miles per hour over: $151
• more than 9 miles per hour to no more than 14 miles per hour over: $226
• more than 14 miles per hour to no more than 19 miles per hour over: $276
• more than 19 miles per hour to no more than 29 miles per hour over: $301
• more than 29 miles per hour over: $376

write and graph a step - function that represents the relationship between the number x of miles per hour over the speed limit and the cost y (in dollars) of the speeding ticket. (see example 4.)

Explanation:

Step1: Define the intervals and corresponding costs

For \(0\leq x\leq9\), \(y = 151\); for \(9 29\), \(y=376\). The step - function can be written as:
\[y=

$$\begin{cases} 151, &0\leq x\leq9\\ 226, &9 29 \end{cases}$$

\]

Step2: Graph the step - function

On the x - axis, we mark the values of \(x\) (miles per hour over the speed limit) and on the y - axis, we mark the values of \(y\) (cost of the ticket in dollars).
For the interval \(0\leq x\leq9\), we draw a horizontal line segment at \(y = 151\) from \(x = 0\) to \(x=9\) (including both endpoints, so we use closed - circles at both ends).
For the interval \(99\)) to \(x = 14\) (closed - circle).
For the interval \(14For the interval \(19For \(x>29\), we draw a horizontal line segment at \(y = 376\) starting from \(x = 29\) (open - circle) and extending to the right.

Answer:

The step - function is \(y=

$$\begin{cases} 151, &0\leq x\leq9\\ 226, &9 29 \end{cases}$$

\) and the graph is as described above.