Math 1101 Eam 1 Practice Problems These problems are not intended to cover all possible test topics. Rather, the should serve as an activit in preparing for our test, but other stud is required to full prepare. These problems contain some multiple choice questions, please consult with our instructor for particular details about our section s test. For questions 1-2, determine whether the given relationship defines a function. Eplain our answer. 1. The temperature t on a backard thermometer at 5 pm on a given da. 2. The temperature t on a backard thermometer on a given da. 3. 1 9 1 7 2 1 3 8 Does the table define as a function of? What about as a function of? 4. Decide whether or not the graph is or is not that of a function. Yes No 5. Decide whether or not the set of unordered pairs defines a function: {( 3, 7), ( 2, 2), (2, 2), (7, 2)} Yes No 6. Decide whether or not the equation = 2 2 defines as a function of. Yes No 1
7. Craft Bill s Cool Car Sales opened as a used car sales lot in 1991. The graph shows the number of cars sold as a function of time. What is the domain of this function if we consider the indicated points? 900 800 700 600 500 400 300 200 100 1991 1992 1993 1994 1995 8. Emploees of a publishing compan received an increase of salar of 7% plus a bonus of $900. Let S() = 1.07 + 900 represent the new salar in terms of the previous salar. Find an interpret S(13000). $13,900: If an emploee s old salar was $13,000, then his/her new salar was $13,900 after the $23,000: If an emploee s old salar was $23,000, then his/her new salar was $13,000 after the $11,308: If an emploee s old salar was $11,308, then his/her new salar was $13,000 after the $14,810: If an emploee s old salar was $13,000, then his/her new salar was $14,810 after the 2
9. The following graph shows the stock price of a new internet compan over the first 18 months after the initial public offering of its stock. Stock Price (in dollars) Month Approimatel in which month(s) did the stock price reach $60? The 2nd and 10th months The 10th and 18th months The price never reached $60 The 18th month 10. Graph the function = 2 + 2 + 1 b plotting points. 11. Graph the function = 3 with a graphing utilit. 6 12. The polnomial 0.0031 4 +0.0051 3 +0.0041 2 +0.15+1.22 gives the predicted sales volume of a compan, in millions of items, where is the number of ears from now. Determine the predicted sales 20 ears from now. Round our answer to the nearest hundredth million. 13. The polnomial function I(t) = 0.1t 2 + 1.4t represents the earl income (or loss) from a real estate investment, where t is the time in ears. After what ear does income begin to decline? 14. Find the slope of the line through the pair of points (2, 6) and (1, 3). 1 3 3 1 3 3 3
15. Decide whether the slope is positive, negative, zero, or undefined. Zero Negative Undefined Positive 16. Find the - and -intercepts of the graph of 3 18 = 18, if the eist. Then graph the equation. 17. Find the slope of the line 6 8 = 16 (if it eists) and the -intercept (if it eists). 18. Graph the equation = 3 2 1. 19. The cost of tuition at a communit college is given b C() = 462 + 50, where is the number of credit hours. Find and interpret the C-intercept of the graph of this function. 50: The tuition increases b $50 for each additional credit hour 462: The tuition increases b $462 for each additional credit hour 50: There is a tuition fee of $50 in addition to the charge per credit hour 462: There is a tuition fee of $462 in addition to the charge per credit hour 20. Assume that the sales of a certain appliance dealer are approimated b a linear function. Suppose that sales were $12,000 in 1982 and $54,000 in 1987. Let = 0 represent 1982. Find the equation giving earl sales S(). S() = 42000 + 54000 S() = 8400 + 54000 S() = 8400 + 12000 S() = 42000 + 12000 21. In one U.S. town the annual consumption, b, in beef (in pounds per person) can be estimated b b = 37 0.6t, where t is the number of ears since 1975. What is the slope of the graph of this function? Write a sentence interpreting its value. 4
22. Does ever line have an -intercept? If not, give an eample of an equation whose graph does not have an -intercept. 23. Write the slope-intercept form of the equation for the line passing through ( 7, 6) and (1, 3). 24. Find the average rate of change for the function = 2 + 5 between = 2 and = 9. 16 14 112 9 18 25. An electrician charges a fee of $40 plus $25 per hour. Let be the cost in dollars of using the electrician for hours. Find the slope-intercept form of the equation. 26. The paired data below consists of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands). Use linear regression to find a linear function that predicts the number of products sold as a function of the cost of advertising. Cost 9 2 3 4 2 5 9 10 Number 85 52 68 67 86 83 73 5
27. The following graph shows data for a recent train ride from New York to Toronto. At What rate did the train travel? Distance from New York (miles) 300 200 100 1 2 3 4 Time of Da (PM) 60 miles per hour 65 miles per hour 50 miles per hour 120 miles per hour 28. Solve the equation 1 6 ( + 18) 1 ( 7) = + 5 7 and then check our answer using a graphing utilit. 133 119 203 294 6
29. The paired data below consists of advertising (in thousands of dollars) and the number of products sold (in thousands). Use linear regression to find a rounded linear function that predicts the number of products sold as a function of the cost of advertising and predict the number of products sold (in thousands) if the cost of advertising is $6000. Cost 9 2 3 4 2 5 9 10 Number 85 52 68 67 86 83 73 16,795,800 products sold 69,540 products sold 72,530 products sold 79,240 products sold 30. Solve the sstem of equations using a graphing aid. { 3 2 = 1 3 + 4 = 29 31. Solve the sstem of equations b hand using an method. { 9 + 6 = 33 2 + 4 = 2 = 3, = 2 = 2, = 2 = 3, = 1 No solution 32. Nadine sold two kinds of tickets to her class pla. Student tickets cost $4.00 each, and adult tickets cost $6.50 each. If Nadine sold a total of 35 tickets for $182.50, how man student tickets did she sell? 18 22 17 20 33. A manufacturer has total revenue given b the function R = 170 and has total cost given b C = 28900+30, where is the number of units produced and sold. Find the break-even number of units for the manufacturer. 1445 units 200 units 140 units 2064 units 7