In the preview assignment, you read about the three different phases of pressing a brake pedal of a car:

When you first begin pressing the brake pedal, there is no braking force $($dead band$).$

After the dead band, you reach a point where the further you press the brake pedal, the greater the braking force.

You reach another point where no matter how much further you press the brake pedal, the braking force remains the same.How do you think that we can express the behavior of the brake pedal as a function? Well, we use

more than one formula $($or other representation$)$ to describe the behavior of the braking force for

these different phases.

Let b$($s$)$ be the braking force applied to the car when the brake pedal is depressed s inches. The

braking force is measured in pounds. Let's graph the function b for a particular car. Suppose that

the braking system of a particular car behaves in the following way:

If s is between $0$ and $0\mathrm{.}2$ inches, the braking force is zero $($dead band$).$

When the s reaches $0\mathrm{.}2$ inches, the braking force begins to increase linearly with a rate of

change of $1000$ pounds per inch.

On the axes below, draw the graph of the function b for s