Chap7 Section7

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

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Section 7.7 Solving Rational Equations 723 Version: Fall 2007 7.7 Exercises For each of the rational functions given in Exercises 1 - 6 , perform each of the following tasks. i. Set up a coordinate system on graph paper. Label and scale each axis. Re- member to draw all lines with a ruler. ii. Plot the zero of the rational function on your coordinate system and label it with its coordinates. Plot the verti- cal and horizontal asymptotes on your coordinate system and label them with their equations. Use this informa- tion (and your graphing calculator) to draw the graph of f . iii. Plot the horizontal line y = k on your coordinate system and label this line with its equation. iv. Use your calculator’s intersect util- ity to help determine the solution of f ( x ) = k . Label this point on your graph with its coordinates. v. Solve the equation f ( x ) = k alge- braically, placing the work for this solution on your graph paper next to your coordinate system containing the graphical solution. Do the answers agree? 1. f ( x ) = x 1 x + 2 ; k = 3 2. f ( x ) = x + 1 x 2 ; k = 3 3. f ( x ) = x + 1 3 x ; k = 2 4. f ( x ) = x + 3 2 x ; k = 2 5. f ( x ) = 2 x + 3 x 1 ; k = 3 Copyrighted material. See: http://msenux.redwoods.edu/IntAlgText/ 1 6. f ( x ) = 5 2 x x 1 ; k = 3 In Exercises 7 - 14 , use a strictly alge- braic technique to solve the equation f ( x ) = k for the given function and value of k . You are encouraged to check your result with your calculator. 7. f ( x ) = 16 x 9 2 x 1 ; k = 8 8. f ( x ) = 10 x 3 7 x + 7 ; k = 1 9. f ( x ) = 5 x + 8 4 x + 1 ; k = 11 10. f ( x ) = 6 x 11 7 x 2 ; k = 6 11. f ( x ) = 35 x 7 x + 12 ; k = 5 12. f ( x ) = 66 x 5 6 x 10 ; k = 11 13. f ( x ) = 8 x + 2 x 11 ; k = 11 14. f ( x ) = 36 x 7 3 x 4 ; k = 12 In Exercises 15 - 20 , use a strictly alge- braic technique to solve the given equa- tion. You are encouraged to check your result with your calculator. 15. x 7 + 8 9 = 8 7 16. x 3 + 9 2 = 3 8
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724 Chapter 7 Rational Functions Version: Fall 2007 17. 57 x = 27 40 x 2 18. 117 x = 54 + 54 x 2 19. 7 x = 4 3 x 2 20. 3 x 2 = 5 3 x For each of the rational functions given in Exercises 21 - 26 , perform each of the following tasks. i. Set up a coordinate system on graph paper. Label and scale each axis. Re- member to draw all lines with a ruler. ii. Plot the zero of the rational function on your coordinate system and label it with its coordinates. You may use your calculator’s zero utility to find this, if you wish. iii. Plot the vertical and horizontal as- ymptotes on your coordinate system and label them with their equations. Use the asymptote and zero informa- tion (and your graphing calculator) to draw the graph of f . iv. Plot the horizontal line y = k on your coordinate system and label this line with its equation. v. Use your calculator’s intersect util- ity to help determine the solution of f ( x ) = k . Label this point on your graph with its coordinates.
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