Answer
See the graph below
b) 8 sq units
Work Step by Step
Four series of transformation to $y = |x|$
1. Shift right by 4 units, this gives $y = |x-4|$
2. Multiply y by 2 for each x we get $y = 2|x-4|$
3. Reflect the graph about x-axis and we get $y = -2|x-4|$
4. Finally raise the graph by 4 units we get $y = -2|x-4| +4$
b)
Area bounded by f and x-axis above x-axis
= Area of Triangle ABC = $\frac{1}{2}\times4\times4 = 8$
