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Unformatted text preview: 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...
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 Rational Functions, strictly algebraic technique

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