Chap2 Section4

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

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Section 2.4 Solving Equations and Inequalities by Graphing 153 Version: Fall 2007 2.4 Exercises In Exercises 1 - 6 , you are given the de- finition of two functions f and g . Com- pare the functions, as in Example 1 of the narrative, at the given values of x . 1. f ( x ) = x +2 , g ( x ) = 4 x at x = 3 , 1, and 2. 2. f ( x ) = 2 x 3 , g ( x ) = 3 x at x = 4 , 2, and 5. 3. f ( x ) = 3 x , g ( x ) = x +9 at x = 4 , 3 , and 2 . 4. f ( x ) = x 2 , g ( x ) = 4 x + 5 at x = 2 , 1 , and 6 . 5. f ( x ) = x 2 , g ( x ) = 3 x 2 at x = 3 , 1 , and 0 . 6. f ( x ) = | x | , g ( x ) = 4 x at x = 1 , 2 , and 3 . In Exercises 7 - 12 , perform each of the following tasks. Remember to use a ruler to draw all lines. i. Make an accurate copy of the image on graph paper (label each equation, label and scale each axis), drop a dashed vertical line through the point of in- tersection, then label and shade the solution of f ( x ) = g ( x ) on the x -axis. ii. Make a second copy of the image on graph paper, drop a dashed, vertical line through the point of intersection, then label and shade the solution of f ( x ) > g ( x ) on the x -axis. Use set- builder and interval notation to de- scribe your solution set. iii. Make a third copy of the image on Copyrighted material. See: 1 graph paper, drop a dashed, vertical line through the point of intersection, then label and shade the solution of f ( x ) < g ( x ) on the x -axis. Use set- builder and interval notation to de- scribe your solution set. 7. x 5 y 5 f g 8. x 5 y 5 f g

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154 Chapter 2 Functions Version: Fall 2007 9. x 5 y 5 f g 10. x 5 y 5 f g 11. x 5 y 5 f g 12. x 5 y 5 f g In Exercises 13 - 16 , perform each of the following tasks. Remember to use a ruler to draw all lines. i. Make an accurate copy of the image on graph paper, drop dashed, verti- cal lines through the points of inter- section, then label and shade the so- lution of f ( x ) g ( x ) on the x -axis. Use set-builder and interval notation to describe your solution set. ii. Make a second copy of the image on graph paper, drop dashed, vertical lines through the points of intersection, then label and shade the solution of f ( x ) < g ( x ) on the x -axis. Use set-builder and interval notation to describe your solution set.
Section 2.4 Solving Equations and Inequalities by Graphing 155 Version: Fall 2007 13. x 5 y 5 f g 14. x 5 y 5 f g 15. x 5 y 5 f g 16. x 5 y 5 f g In Exercises 17 - 20 , perform each of the following tasks. Remember to use a ruler to draw all lines. i. Load each side of the equation into the Y= menu of your calculator. Ad- just the WINDOW parameters so that the point of intersection of the graphs is visible in the viewing window. Use the intersect utility in the CALC menu of your calculator to determine the x-coordinate of the point of intersec- tion. ii. Make an accurate copy of the image in your viewing window on your home- work paper. Label and scale each axis with xmin, xmax, ymin, and ymax, and label each graph with its equa- tion.

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