852 CHAPTER 11 Systems of Equations and Inequalities In Problems 1–6, solve each equation. 1. − = x x 2 0 2 2. + = x3 1 4 3. − − − = x x x 2 3 8 3 0 3 2 4. = + 3 9 x x 1 5. ( ) ( ) − + + = x x log 1 log 2 1 2 3 3 6. = e 3x Cumulative Review In Problems 21 and 22, solve each system of equations. 21. + = = ⎧ ⎨ ⎪⎪⎪ ⎩ ⎪⎪⎪ x y y x 3 12 9 2 2 2 22. − = − = ⎧ ⎨ ⎪⎪⎪ ⎩ ⎪⎪⎪ y x y x 2 3 5 1 2 2 23. Graph the system of inequalities: + ≤ − ≥ ⎧ ⎨ ⎪⎪⎪ ⎩ ⎪⎪⎪ x y x y 100 4 3 0 2 2 In Problems 24 and 25, find the partial fraction decomposition of each rational expression. 24. ( ) + + x x 3 7 3 2 25. ( ) − + x x x 4 3 3 2 2 2 26. Graph the system of inequalities. State whether the graph is bounded or unbounded, and label all corner points. ≥ ≥ + ≥ − ≥ ⎧ ⎨ ⎪⎪ ⎪⎪ ⎪ ⎩ ⎪⎪ ⎪⎪ ⎪⎪ x y x y x y 0 0 2 8 2 3 2 27. Maximize = + z x y 5 8 subject to the constraints ≥ x 0, + ≤ x y 2 8, and − ≤− x y3 3. 28. Megan went clothes shopping and bought 2 pairs of jeans, 2 camisoles, and 4 T-shirts for $90.00. At the same store, Paige bought one pair of jeans and 3 T-shirts for $42.50, while Kara bought 1 pair of jeans, 3 camisoles, and 2 T-shirts for $62.00. Determine the price of each clothing item. 7. Determine whether the function ( ) = + g x x x 2 1 3 4 is even, odd, or neither. Is the graph of g symmetric with respect to the x-axis, y-axis, or origin? 8. Find the center and radius of the circle + − + − = x y x y 2 4 11 0 2 2 Graph the circle. 9. Graph ( ) = + − f x 3 1 x 2 using transformations.What are the domain, range, and horizontal asymptote of f ? 10. The function ( ) = + f x x 5 2 is one-to-one. Find −f .1 Find the domain and the range of f and the domain and the range of −f .1 11. Graph each equation. (a) = + y x3 6 (b) + = x y 4 2 2 (c) = y x3 (d) = y x 1 (e) = y x (f) = y ex (g) = y x ln (h) + = x y 2 5 1 2 2 (i) − = x y3 1 2 2 (j) − − + = x x y 2 4 1 0 2 12. ( ) = − + f x x x3 5 3 (a) Using a graphing utility, graph f and approximate the zero(s) of f. (b) Using a graphing utility, approximate the local maxima and the local minima. (c) Determine the intervals on which f is increasing.
RkJQdWJsaXNoZXIy NjM5ODQ=