TEST 1 REVIEW ----------MATH 1324 1. Is the relation defined by the table a function of x? Write down the sets of domain and range. x 1 2 6 8 11 y -4 -4 5 16 5 2. Which of the graphs below represent y as a function of x? (a) (b) a. both (a) and (b) b. neither (a) nor (b) c. only (b) d. only (a) ANSWER: c 3. If , is y a function of x? a. Yes b. No ANSWER: Yes 4. If , is y a function of x? a. Yes b. No ANSWER: No 5. If , find . and , find a. -2 b. 0 c. -2000 d. -200 e. 100 ANSWER: b 6. If and simplify. a. b. c. d. e. ANSWER: d 7. State the domain and range of the function below a. Domain: real numbers 2 Range: real numbers 2 b. Domain: real numbers > 2 Range: real numbers > 2 c. Domain: all real numbers Range: all real numbers d. Domain: real numbers 2 Range: real numbers 0 e. Domain: real numbers 0 Range: real numbers 0 = 2 ANSWER: d 8. State the domain and range of the function below. a. domain: real numbers range: real numbers b. domain: all reals range: real numbers c. domain: real numbers range: all reals d. domain: all reals range: real numbers e. domain: real numbers range: real numbers ANSWER: d 9. A function and its graph are given. Find the domain. 10. For and 11. For , find and , find , , . a. b. c. d. e. ANSWER: c 12. Choose the equation of the line with the given slope and y-intercept. slope: y-intercept a. b. c. d. e. ANSWER: c : 13. Determine whether the following pairs of equations represent parallel lines, perpendicular lines, or neither of these. 3x - 7y = 3 9x - 21y = 3 a. parallel lines b. perpendicular lines c. neither ANSWER: a 14. Determine whether the following pairs of equations represent parallel lines, perpendicular lines, or neither of these. a. parallel lines b. perpendicular lines c. neither ANSWER: c 15. Use a graphing utility with the standard viewing window function. 16. Solve the system of equations by any convenient method. a. (-30,11) b. (2,-30) c. (-14,11) d. (2,-14) e. (11,2) ANSWER: d and to graph the 17. Use the left-to-right elimination method to solve the system. a. b. c. d. e. solution: solution: solution: solution: solution: ANSWER: b 18. A linear cost function is , where x represents the number of units produced. What is the cost of producing one more item if 100 are currently being produced? Round your answer to the nearest cent. a. $8,545.97 b. $28.97 c. $5,620.00 d. $5,648.97 e. $100.00 ANSWER: b 19. A linear revenue function is , where x represents the number of units sold. What is the revenue received from selling one more item if 50 are currently being sold? Round your answer to the nearest cent. a. $1,377.00 b. $50.00 c. $1,350.00 d. $27.00 e. $2,079.00 ANSWER: d 20. A company charting its profits notices that the relationship between the number of units sold x and the profit is linear. If 100 nits sold results in $2,900 profit and 150 units sold results in $6,000 profit. Use these two points on the graph of to find the marginal profit. a. $29.00 b. $62.00 c. $40.00 d. $19.33 e. $60.00 ANSWER: b 21. A small business recaps and sells tires. The business has a revenue function and a cost function , where x represents the number of sets of four tires recapped and sold. Find the number of sets of recaps that must be sold to break even. a. 100 b. 500 c. 15 d. 300 e. 80 ANSWER: a 22. Financial Paper, Inc. is a printer of checks and forms for financial institutions. For individual accounts, boxes of 200 checks cost $0.8 per box to print and package; they sell for $4.95 each. Financial Paper's monthly fixed costs for printing and packaging these checks for individuals are $1,415. Which of the following is the equation for the profit function where x denotes the number of boxes of checks produced and sold? a. b. c. d. e. ANSWER: d 23. Assume that the price for a pair of shoes has been set at $30. The demand for a pair of shoes is given by 3p +7q =300 and the supply for the same pair of shoes is p - 3q = 9. In both cases p is price per pair and q is the quantity produced or sold. Compare the quantity demanded and the quantity supplied. Will there be a surplus or shortfall at this price? a. There will be a shortfall. b. There will be a surplus. 24. Find the exact real solutions of the equation a. and b. and c. and , if they exist. d. and e. Real solutions do not exist. ANSWER: b 25. The daily profit from the sale of a product is given by dollars. What is the maximum possible profit? Round intermediate calculations and final answer to the nearest dollar. a. $1,701 b. $2,613 c. $808 d. $95 e. $185 ANSWER: c 26. Sketch the graph of the function y = |x - 2| +2 2 < 0 27. If + 3 0 < 2 6 2 , find f(-4) , f(2), and f(1) 28. Find the equation of the linear function that is the best fit for the given data. Round your final values to one decimal place. x -1 0 1 2 3 4 5 y -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5