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Homework Sheet Section 2.1 1. Write an algebraic equation and solve: An HMO pamphlet contains the following recommended weight for women: “Give yourself 100 pounds for the first 5 feet plus 5 pounds for every inch over 5 feet tall.” Using this description, what height corresponds to a recommended weight of 135 pounds? 2. Perform the indicated operations and write the result in standard form: 6 12 48 3. Solve by the method of your choice: 1 1 1 x x2 3 4. Solve the polynomial equation by factoring and then using the zero-product principle: 2 x 3 8x3 12 x 2 . 5. Solve the equation with rational exponents. Check all proposed solutions. 3 2 ( x) 8 6. Solve the linear inequality. Use interval notation to express the solution set, and graph each solution on the number line (other than ). 4( x 1) 2 3x 6 7. Solve the absolute value inequality: 12 2 x 6 3 7 7 8. Solve the polynomial inequality. Graph the solution set on a real number line and express the solution in interval notation. ( x 7)( x 3) 0 9. Solve the rational inequality and graph the solution set on a real number line. Also express the solution set in interval notation. x 0 x 3 10.Determine whether the relation is a function. Give the domain and range. {(3, -2), (5, -2), (7, 1), (4, 9)} 11.Determine whether the equation defines y as a function of x. x 2 y 16 12.Evaluate the function at the give values of the independent variable and simplify. g ( x) x 2 2 x 3 a) g(-1) b) g(x+5) c) g(-x) 13.Graph the given functions, f and g, in the same rectangular coordinate system. Select integers for x, starting with –2 and ending with 2. Once you have obtained your graphs, describe how the graph of g is related to the graph of f. f ( x) x , g ( x) x 2 14. Use the vertical line test to identify if the graph is one for which y is a function of x. y x 15. Use the graph of f to find the indicated function value. f(-2) Answers: 1. 2. 5 ft 7 in 3. {2 10} 4. 5. 6. 7. 8. 1 3 i 8 24 1 1 3 , , 2 2 2 {4} [0,∞) [ 0 75 87 , , 14 14 [-3,7] -3 9. 7 (-∞,0] or (3,∞) ] 0 10. 11. 12. function; {3,4,5,7}; {-2,1,9} y is a function of x a. 2 b. x2+12x+38 13. 14. 15. not a function -4 c. x2 2 x 3 ( 3