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.
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