Part 3/5:
- The second segment, ( f(x) = x^2 ), begins immediately after ( x = 1 ) at the open circle, marking that while we reach (1, 1), this point is not part of the line or defined under the first equation.
Another Example: Absolute Value Functions
Another common example of a piecewise function is the absolute value function. It can be defined as:
( f(x) = -x ) if ( x < 0 )
( f(x) = x ) if ( x \geq 0 )
When graphed, this function produces a "V" shape, where for negative values of ( x ), the values are reflected across the x-axis, demonstrating the property that absolute values are always positive.
Analyzing a More Complex Example
Consider a more complex graph structured as follows:
- The line starts at (0, 1) and extends in the first quadrant to (1, 2).