Part 4/5:
From (1, 2) to (2, 1), we have a declining straight line, and finally,
For values greater than or equal to 2, the function is flat at ( y = 1 ) extending to infinity.
Determining the Equations
Analyzing such a graph involves identifying intervals where the slope changes. For the depicted graph:
- For ( 0 \leq x < 1 ):
- The equation is ( f(x) = 1 + x )
- For ( 1 \leq x < 2 ):
- The equation is ( f(x) = 3 - x )
- For ( x \geq 2 ):
- The function is simply ( f(x) = 1 )
Each piece needs to be determined based on its slope and position, which may involve identifying where the function is undefined or has different behaviors.