Chapter 9: Exercises with Solutions

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

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Section 9.1 The Square Root Function 879 Version: Fall 2007 9.1 Exercises In Exercises 1 - 10 , complete each of the following tasks. i. Set up a coordinate system on a sheet of graph paper. Label and scale each axis. ii. Complete the table of points for the given function. Plot each of the points on your coordinate system, then use them to help draw the graph of the given function. iii. Use di ff erent colored pencils to project all points onto the x - and y -axes to determine the domain and range. Use interval notation to describe the do- main of the given function. 1. f ( x ) = - x x 0 1 4 9 f ( x ) 2. f ( x ) = - x x 0 - 1 - 4 - 9 f ( x ) 3. f ( x ) = x + 2 x - 2 - 1 2 7 f ( x ) 4. f ( x ) = 5 - x x - 4 1 4 5 f ( x ) Copyrighted material. See: 1 5. f ( x ) = x + 2 x 0 1 4 9 f ( x ) 6. f ( x ) = x - 1 x 0 1 4 9 f ( x ) 7. f ( x ) = x + 3 + 2 x - 3 - 2 1 6 f ( x ) 8. f ( x ) = x - 1 + 3 x 1 2 5 10 f ( x ) 9. f ( x ) = 3 - x x - 6 - 1 2 3 f ( x ) 10. f ( x ) = - x + 3 x - 3 - 2 1 6 f ( x )
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880 Chapter 9 Radical Functions Version: Fall 2007 In Exercises 11 - 20 , perform each of the following tasks. i. Set up a coordinate system on a sheet of graph paper. Label and scale each axis. Remember to draw all lines with a ruler. ii. Use geometric transformations to draw the graph of the given function on your coordinate system without the use of a graphing calculator. Note: You may check your solution with your calculator, but you should be able to produce the graph without the use of your calculator. iii. Use di ff erent colored pencils to project the points on the graph of the func- tion onto the x - and y -axes. Use in- terval notation to describe the domain and range of the function. 11. f ( x ) = x + 3 12. f ( x ) = x + 3 13. f ( x ) = x - 2 14. f ( x ) = x - 2 15. f ( x ) = x + 5 + 1 16. f ( x ) = x - 2 - 1 17. f ( x ) = - x + 4 18. f ( x ) = - x + 4 19. f ( x ) = - x + 3 20. f ( x ) = - x + 3 21. To draw the graph of the function f ( x ) = 3 - x , perform each of the fol- lowing steps in sequence without the aid of a calculator. i. Set up a coordinate system and sketch the graph of y = x . Label the graph with its equation. ii. Set up a second coordinate system and sketch the graph of y = - x . Label the graph with its equation. iii. Set up a third coordinate system and sketch the graph of y = - ( x - 3) . Label the graph with its equation. This is the graph of f ( x ) = 3 - x . Use interval notation to state the domain and range of this function. 22. To draw the graph of the function f ( x ) = - x - 3 , perform each of the following steps in sequence. i. Set up a coordinate system and sketch the graph of y = x . Label the graph with its equation. ii. Set up a second coordinate system and sketch the graph of y = - x . Label the graph with its equation. iii. Set up a third coordinate system and sketch the graph of y = - ( x + 3) . Label the graph with its equation. This is the graph of f ( x ) = - x - 3 . Use interval notation to state the domain and range of this function.
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