Question

the absolute value function as price wise-defined function with the linear parts
f(x)=|3x+1|

Answer 1

The absolute value function can be defined as a piecewise-defined function with the linear parts as follows for the given function:

For x ≤ -1:
f(x) = -(3x + 1)

For x > -1:
f(x) = 3x + 1