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. 9. f ( x ) = | x 1 | 10. f ( x ) = | x + 2 | 11. g ( x ) = | 2 x 1 | 12. g ( x ) = | 5 2 x | 13. h ( x ) = | 1 3 x | 14. h ( x ) = | 2 x + 1 | 15. f ( x ) = x − | x | 16. f ( x ) = x + | x 1 | 17. Use a graphing calculator to draw the graphs of y = | x | , y = 2 | x | , y = 3 | x | , and y = 4 | x | on the same viewing win- dow. In your own words, explain what you learned in this exercise. 18. Use a graphing calculator to draw the graphs of y = | x | , y = (1 / 2) | x | , y = (1 / 3) | x | , and y = (1 / 4) | x | on the same viewing window. In your own words, ex- plain what you learned in this exercise. 19. Use a graphing calculator to draw the graphs of y = | x | , y = | x 2 | , y = | x 4 | , and y = | x 6 | on the same view- ing window. In your own words, explain what you learned in this exercise. 20. Use a graphing calculator to draw the graphs of y = | x | , y = | x + 2 | , y = | x +4 | , and y = | x +6 | on the same view- ing window. In your own words, explain what you learned in this exercise.
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368 Chapter 4 Absolute Value Functions Version: Fall 2007 In Exercises 21 - 36 , perform each of the following tasks. Feel free to check your work with your graphing calculator, but you should be able to do all of the work by hand. i. Set up a coordinate system on a sheet of graph paper. Label and scale each axis. Create an accurate plot of the function y = | x | on your coordinate system and label this graph with its equation. ii. Use the technique of Examples 12, 13, and 14 in the narrative to help se- lect the appropriate geometric trans- formations to transform the equation y = | x | into the form of the func- tion given in the exercise. On the same coordinate system, use a differ- ent colored pencil or pen to draw the graph of the function resulting from your applied transformation. Label the resulting graph with its equation. iii. Use interval notation to describe the domain and range of the given func- tion.
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