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Unit 4 Rational functions

Unit 4 Rational functions. 8-6 Solving rational expressions. Solving Rational Equations. To solve a rational equation first multiply each side by the LCD. You must check for extraneous solutions. (A solution that doesn’t work). LCD?. SOLVE:. Multiply by LCD. SOLVE.

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Unit 4 Rational functions

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  1. Unit 4 Rational functions 8-6 Solving rational expressions

  2. Solving Rational Equations • To solve a rational equation first multiply each side by the LCD. • You must check for extraneous solutions. (A solution that doesn’t work)

  3. LCD? SOLVE: Multiply by LCD SOLVE Check for Extraneous solutions. (plug answer into original problem

  4. SOLVE: LCD? CHECK ?? -1 does not work so there is NO SOLUTION

  5. How to solve using the CALC. • Set equal to zero and graph (have to use parenthesis. • Y2 = 0 • Find where the graph crosses x-axis (2nd trace intersect). Answer: X=0 Answer: X= 1, -1 Answer: X= -2

  6. Practice • Pg 546 #8-19(all), 44-52(even)

  7. Word Problems • The function below gives the concentration of the saline solution after adding x milliliters of 0.5% solution to 100 milliliters of 2% solution. • How man ML of the 0.5% solution must be added to have a combined concentration of 0.9%? Answer: (graph? solve by hand) X=275

  8. You earn a 75% on the first test of the quarter how many consecutive 100% test scores do you need to bring your test average up to a 95%? Write a rational function. Find when the rational function will be 95% Answer: To find the average of something: add and divide by total number Answer: (graph) You will need to make 100% on the next 4 test to bring your test average up to a 95%

  9. Distance = rate x time When a problem involves “how fast”, “how far”, or “for how long”, think about distance equation d =rt • A plane flies 1850 miles at a speed of 480 mph. Find the time of the trip to the nearest hundredth. • On the return trip the plane travels at the same speed (480) but a tail wind helps the plane move faster. The total flying time for the round trip is 7.55 hours. Find the speed x of the tail wind. Answer: Answer:

  10. Work Problems • “you have to think of the problem in terms of how much each person or thing does in a given amount of time” Joe can paint a room in 8 hours and Steve can paint the same room in 12 hours. How long will it take the two to paint the room if they work together? Working together Mary and Sally can paint a fence in 5.14 hours. Working alone Mary can paint the fence in 9 hours. How long would it take Sally to paint the fence alone? How much of the job can Joe do in one hour? Steve?

  11. Practice • Pg 521 #35, 39, 40, 46* • Pg 545 #20,36,37,38,39

  12. A plane leaves Chicago and flies to San Francisco (1850 miles away) with a headwind The same plane returns to Chicago with a tailwind. The round trip took 7.75 hours.If the airplane cruises at 480 mph, what is the speed of the wind? (Assume the winds are constant.) Rate * time = distance Time of a trip equals the distance over speed X=wind speed San Francisco Chicago Solve by Graphing Zoom fit, x-max to 50 Write an equation X = 35.195

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