The area of the region bounded by `y=|x-1|and y=3-|x|,` is

Options

A. 2
B. 3
C. 4
D. 1

Answer

To find the area of the region bounded by the curves \( y = |x - 1| \) and \( y = 3 - |x| \), we will follow these steps:

### Step 1: Understand the Functions
The first function is \( y = |x - 1| \). This can be expressed as:
- \( y = x - 1 \) for \( x \geq 1 \)
- \( y = -x + 1 \) for \( x < 1 \)

The second function is \( y = 3 - |x| \). This can be expressed as:
- \( y = 3 - x \) for \( x \geq 0 \)
- \( y = 3 + x \) for \( x < 0 \)