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MATH 110

MATH 110. Review. Jeopardy. Final Jeopardy?. Final Exam: Monday December 12 th , 2005 8:00am to 10:00am Room S SCI 100 Get to the exam no later than 7:30am. x. 2. -2. 0. 2. 4. y. 5. 4. 3. 2. 1. x. 1. 2. 1. 4. 5. y. 0. 3. -2. 1. 9. x. 1. 2. -3. 4. 6. y. 3. 1.

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MATH 110

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  1. MATH 110 Review

  2. Jeopardy

  3. Final Jeopardy? • Final Exam: • Monday December 12th, 2005 • 8:00am to 10:00am • Room S SCI 100 • Get to the exam no later than 7:30am

  4. x 2 -2 0 2 4 y 5 4 3 2 1 x 1 2 1 4 5 y 0 3 -2 1 9 x 1 2 -3 4 6 y 3 1 3 -1 5 Functions 100 • Which of the tables express y as a function of x? • Answer: 1st and 4th

  5. Functions 200 • Find the domain of the function given below: • Answer: [0,3)

  6. Functions 300 • The graphs of f(x) and g(x) are shown. • Find the domain and range of each function • Answer: f(x) D: [-3,infinity) R: [-4,infinity) g(x) D: [-5,5] R: [-3,3] f(x) g(x)

  7. Functions 400 • Which of the functions shown has a domain of all real numbers except 18? • Answer: g(x)

  8. Functions 500 • A 24 inch wire is cut into 4 pieces to form a rectangle whose shortest side has a length of x. Express the area of this rectangle as a function of x. What is the domain of this function? • Answer:

  9. Straight as an Arrow 100 • Suppose that the quantity sold, q, of a particular product can be expressed as a linear function of the product’s price, p, by the linear function q(p) = -50p + 2000. Determine the slope of the graph of q(p) and interpret the slope in practical terms. • Answer: slope is -50; this means that the amount sold decreases by 50 when the product’s price increase by $1.00.

  10. Straight as an arrow 200 • Find the coordinates of the x and y intercepts of 3x + 7y -1 =0. • Answer: x-int (1/3,0) ; y-int (0, 1/7)

  11. Straight as an arrow 300 • A small electrical co-op in rural Arizona charges its customers a $5.00 basic monthly fee plus $0.12 per kilowatt hour used. Write a function to represent the monthly charge in dollars on an electric bill in terms of the number of kilowatt hours used. • Answer: f(x) = 0.12x+5.00

  12. Straight as an arrow 400 • Determine whether the following table is a linear function. If it is find the equation of the line. • Answer: yes constant rate of change; equation y = 2.1x +0.9

  13. Straight as an arrow 500 • Find the equation of the line perpendicular to 2x – y = 3 which passes through the point (1,3). • Answer: y = -0.5(x-1)+3

  14. Word Problems 100 • A couple invests $3500 to build a rose garden. On average, it costs them $0.35 to grow each rose. If each rose can be sold for $1.75, how many roses must be sold to break even? • Answer: 2500 roses

  15. Word Problems 200 • A shop owner wants to mix high quality coffee beans that cost $5.00 per pound with cheap, crummy tasting beans that cost $1.00 per pound to get 20 pounds of a blend which should be worth $3.50 per pound. How much of the cheap blend should be used? • Answer: 7.5 pounds

  16. Word Problems 300 • You invest $1000 in two accounts. The first pays 6% annual interest, the other pays 9% annual interest. At the end of one year you collect $84.60 in interest. How much was invested in each account? • Answer: $180 in the 6% account and $820 in the 9% account.

  17. Word Problems 400 • A train that is traveling 52 mph leaves the station and goes west. Another train leaves the station on a parallel track 1 hour later traveling west at 65 mph. How long until the fast train catches up with the slow train? • Answer: 5 hours

  18. Word Problems 500 • A rancher wishes to enclose two adjacent rectangular corrals such that the right-hand corral has twice the length of the left hand (see diagram). She has 900 feet of fencing. Express the area of the enclosure as function of the length. Answer:

  19. Pieces 100 Which of the following represents the piece-wise function shown below? Answer: c

  20. Pieces 200 • Sketch the graph of the piece-wise defined function shown below:

  21. Pieces 300 • Find g(0) for the function given below: • Answer: -2

  22. Pieces 400 • Write the piece-wise function for the graph shown: • Answer:

  23. Pieces 500 • The following table gives the Tax Rate Schedule for a person whose filing status was single during the year 2003. • Determine a formula for the tax a person would pay with an adjusted gross income that is between $28,400 and $68,800 • Answer: 3910+0.25(x-28400)

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