Math 150 T2-Piecewise-Defined Functions Review                                      Page 1
                                        MATH150–TOPIC2
                               PIECEWISE-DEFINED FUNCTIONS
                       I.  Absolute Value Functions
                      II.  Piecewise Functions
                           Practice Problems
        Math 150 T2-Piecewise-Defined Functions Review                                      Page 2
           I.   Absolute Value Functions
                Sometimesafunctioncannotbedefinedasasingleexpression. Theabsolute
                value function is a good example of this. Recall that f(x)=|x| is defined
                by two equations: f(x)=x if x ≥ 0andf(x)=−x if x<0. These two
                ‘pieces’ can be written as follows
               f(x)=|x| = ( x if x ≥ 0            −→           −x                   x
                                −x if x<0.
                Exercise 1:     Write a piecewise definition for f(x)=|x − 3|.Sketchthe
                graph of f.                                                                Answer
                Here’s a more complicated absolute value function.
                Example: Define and sketch g(x)=|x|.
                                                           x
                                       x
                                       =1 ifx>0
                Definition: g(x)= x                                 Note: g(0) is undefined.
                                      −x
                                       x =−1ifx<0.
                                                    1 ◦
                                                      ◦ −1
        Math 150 T2-Piecewise-Defined Functions Review                                       Page 3
          II.   Piecewise Functions
                Let’s analyze the piecewise function defined by
                                            
                                            −x+1,x≤−1
                                   f(x)= 2,              −1