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Section 1.2

Section 1.2. 1. Yes it is a function. It passes the vertical line test. 2. No it is not a function. It fails the vertical line test. 3. Yes it is a function. It passes the vertical line test. 4-7 Evaluate the given expression Find the domain of the function Find the range

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Section 1.2

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  1. Section 1.2 1. Yes it is a function. It passes the vertical line test.

  2. 2. No it is not a function. It fails the vertical line test.

  3. 3. Yes it is a function. It passes the vertical line test.

  4. 4-7 • Evaluate the given expression • Find the domain of the function • Find the range • (hint: use a graphing calculator) Find f (10) 4. • The domain is determined by the square root. The quantity inside the root sign must not be negative so x – 1 ≥ 0 or x ≥ 1. • Range from a calculator y ≥ 0.

  5. 5. , find b. Find the domain. The problem is that the function includes division so we must make sure we are not dividing by 0. z + 4 ≠ 0 or z ≠ - 4. c. The range from a calculator is y ≠ 0.

  6. 6. , find b. Find the domain. The problem is that the function includes an even rood so we must make sure that the base is not negative and since the base in x then x ≥ 0. c. The range from a calculator is y ≥ 0.

  7. 7. OR use your calculator. From calculator.

  8. 8-9 Graph each function. 8.

  9. 9.

  10. 10 • Graph the function in an appropriate window. (answers may vary) • Find the vertex. a. b. Using a calculator and minimum V (- 20, 100). My window is - 60 ≤ x ≤ 10 and -100 ≤ y ≤ 1000

  11. 11 – 15 Solve each equation by factoring, completing the square, using your calculator or the Quadratic formula, as you wish. 11.

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  14. 14.

  15. 15.

  16. 16-18 Solve each equation using a graphing calculator 16. My window is - 5 ≤ x ≤ 6 and -22 ≤ y ≤ 6

  17. 17. My window is - 7 ≤ x ≤ 1 and - 2 ≤ y ≤ 16

  18. 18. My window is - 4 ≤ x ≤ 3 and -9 ≤ y ≤ 15

  19. 19. Business: Cost Functions A lumberyard will deliver wood for $4 per board foot plus a delivery charge of $20. Find a function C (x) for the cost of having x board feet of lumber delivered. The unit cost is $4 per board feet and the fixed cost is the delivery charge of $20. Let x be the number of board feet then the cost C C (x) = 4x + 20

  20. 20. Business: salary An employee’s weekly salary is $500 plus $15 per hour of overtime. Find a function P(x) giving his pay for a week in which he worked x hours of overtime. The overtime salary is $15 per hour and the fixed salary is $500. Let x be the number of overtime hours then the total pay will be the fixed pay plus the overtime pay of P(x) = 500 + 15x

  21. 21. General: Water Pressure At a depth of d feet underwater, the water pressure is • p (d) = 0.45 d + 15 pounds per square inch. Find the pressure at: • The bottom of a 6-foot-deep swimming pool. • The maximum ocean depth of 35,000 feet.

  22. 22. General: Stopping Distance A car traveling at speed v miles per hour on a dry road should be able to come to a full stop in a distance of feet find the stopping distance required for a car traveling at: 40 mph

  23. 23. Biomedical: Cell Growth The number of cells in a culture after t days is given • by . Find the size of the culture after • 2 days • 10 days

  24. 24. Business: Break-Even Points and Maximum Profits A company that produces tracking • devices for computer disks drives finds that if it produces x devices per week, its costs • and its revenue (both in dollars) will be as follows: • Find the company’s break-even points. • Find the number of devices that will maximize profit, and the maximum profit. a. To find the break-even points graph the functions on your calculator and use the intersect function. (40, 23200) and (200, 52000) b. To find the maximum profit graph the profit function P(x) = R(x) – c(x) and find its vertex. The maximum profit of $12,800 occurs at x = 120. My window is 0 ≤ x ≤ 250 and 0 ≤ y ≤ 61000

  25. 25. Behavior Science: Smoking and Education According to a study, the probability • that a smoker will quit smoking increases with the smoker’s educational level. The • probability (expressed as a percent) that a smoker with x years of education will quit • Is approximately y = 0.831x 2 18.1x + 137.3 for 10 ≤ x ≤ 16. • Graph this curve on the window [10,16] by [0,100]. • Find the probability that a high school graduate smoker (x=12) will quit. • Find the probability that a college graduate smoker (x=16) will quit.

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