Part 2/5:
( f(x) = 1 - x ) if ( x \leq 1 )
( f(x) = x^2 ) if ( x > 1 )
In this example, we have two distinct equations: one linear equation for ( x ) less than or equal to 1, and another quadratic equation for values of ( x ) greater than 1. The graph will display a line that decreases and then abruptly changes to a curve, illustrating the transition at ( x = 1 ).
Graphing a Piecewise Function
When graphing piecewise functions, it is crucial to consider the defined intervals. In our previous example, the graph consists of two components:
- The first segment, ( f(x) = 1 - x ), starts at the point (1, 0), which is represented by a closed circle since it includes 1 in the inequality.