Chap4 Section2

# Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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Section 4.2 Absolute Value 367 Version: Fall 2007 4.2 Exercises For each of the functions in Exercises 1 - 8 , as in Examples 7 and 8 in the narra- tive, mark the “critical value” on a num- ber line, then mark the sign of the ex- pression inside of the absolute value bars below the number line. Above the num- ber line, remove the absolute value bars according to the sign of the expression you marked below the number line. Once your number line summary is finished, create a piecewise definition for the given absolute value function. 1. f ( x ) = | x + 1 | 2. f ( x ) = | x 4 | 3. g ( x ) = | 4 5 x | 4. g ( x ) = | 3 2 x | 5. h ( x ) = | − x 5 | 6. h ( x ) = | − x 3 | 7. f ( x ) = x + | x | 8. f ( x ) = | x | x For each of the functions in Exercises 9 - 16 , perform each of the following tasks. i. Create a piecewise definition for the given function, using the technique in Exercises 1 - 8 and Examples 7 and 8 in the narrative. ii. Following the lead in Example 9 in the narrative, use your piecewise defi- nition to sketch the graph of the given function on a sheet of graph paper. Please place each exercise on its own Copyrighted material. See: 1 coordinate system.

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