9'1 Graphing Rational Functions Need Graph Paper

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9.1 Graphing Rational FunctionsNeed Graph
Paper!!!

• Objective
• To graph rational functions.

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• Vocabulary
• Rational Function- the ratio of two polynomial
  expressions
• Vertical Asymptote- excluded values for the
  rational function (what value for x would make
  the denominator undefined)
• Horizontal Asymptote- determine the value of the
  polynomial function as x approaches infinity.
• Discontinuity Point- the graphs of these
  functions appear to have holes

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• Graph the function.
• 1.)
• V.A.
• H.A.

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• Graph the function.
• 2.)
• V.A.
• H.A.

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• Graph the function.
• 3.)
• V.A.
• H.A.

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• Graph the function.
• 4.)
• V.A.
• H.A.

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• Graph the function. (need to do)
• 5.)
• V.A.
• H.A.

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• Assignment 9.1
• Page 554 (19-35 odd), 37, 38, 39, 41, 43

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9.2 Direct, Inverse, and Joint Variation

• Objective
• To solve problems involving direct, inverse, and
  joint variation.

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• Direct Variation- (as y increases, x increases)
  or (as y decreases x decreases).
• Example (as a cars speed increases, brake time
  increases.)
• ykx, kconstant
• Inverse Variation- (as y increases, x decreases)
  or (as y decreases x increases).
• Example (as elevation increases, the temperature
  decreases.)
• Joint Variation- (as y increases the product of x
  and z increase) or ( as y decreases the product
  of x and z decrease)
• Example (as salary increases, the number of
  hours and amount of work increase)
• ykxz

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• 1.) Find y when x6, if y varies directly as x
  and y8 when x2.

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• 2.) Find y when x2.5, if y varies inversely as x
  and x5 when y3

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• 3.) Find y when x6 and z8, if y varies jointly
  as x and z and y60 when x3 and z4.

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• 4.) The pitch of a musical note varies inversely
  as its wavelength. If the tone has a pitch of 440
  vibrations per second and a wavelength of 2.4
  feet, find the pitch of a tone that has a
  wavelength of 1.6 feet.

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• 5.) The amount of oil use by a ship traveling at
  a uniform speed varies jointly with the distance
  and the square of the speed. If the ship uses 500
  barrels of oil in traveling 220 miles at 40 mph,
  determine how many barrels of oil are used when
  the ship travels 400 miles at 25 mph. Round to
  the nearest barrel.

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• Assignment 9.2
• Page 559 (18-23 all), (25- 28), 31 b and c, 32,
  33 c, 35, 36, 38, 39, 40

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9.3 Multiplying and Dividing Rational Expressions

• Objective
• To simplify rational expressions
• To simplify complex fractions

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• Simplify. (Review)
• 1) 2)

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• Simplify. (Multiplying and dividing fractions)
• 3) 4)

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• Simplify. (Multiplying and dividing fractions)
• 5) 6)

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• Simplify. (Multiplying and dividing fractions)
• 7) 8)

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• Assignment 9.3
• Page 566 (17-41 odd), 45, 46, 47, 48, 51

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9.4 Adding and Subtracting Rational Expressions

• Objective
• To find the least common denominator or two or
  more algebraic expressions
• To add and subtract rational expressions

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• Simplify. Find the LCD 1st.
• 1) 2)

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• Simplify. Find the LCD 1st.
• 3) 4)

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• Simplify. Find the of the numerator and
  denominator LCD 1st.
• 5) 6)

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• Assignment 9.4
• Page 573 (21-39 odd), 44, 45, 47, 48, 51

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9.5 Solving Rational Equations and Inequalities

• Objective
• To solve rational equations and Inequalities

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• Solve each equation. Check the solution. (Find
  LCD 1st)
• 1)

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• Solve each equation. Check the solution. (Find
  LCD 1st)
• 2)

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• Solve each inequality. Check the solution. (Find
  LCD 1st)
• 3)

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• Solve each inequality. Check the solution. (Find
  LCD 1st)
• 4)

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5) George can do a job by himself in 4 hours.
Darlene can do a job by herself in 6 hours. How
long will it take them if they work together?
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• 6) Bob can do a job by himself in 5 hours. When
  Ashley and he work together they can do the job
  in 2 hours. How long would it take Ashley
  working by herself to complete the job?

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• 7) Pipe A can fill a pool in 4 hours. Pipe B can
  fill a pool in 6 hours. If both pipes are turned
  on, how long will it take to fill the pool when a
  drain that takes 10 hours to empty the pool is
  accidentally left open?

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• 8) Two numbers are in a ratio of 3 to 4. If the
  numerator is decreased by 10 and the denominator
  is increased by 20, its value is 1/3. Find the
  original fraction.

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• 9) A cyclist travels 8 km in the same time that a
  walker travels 3km. The speed of the cyclist is
  8km/hr more than the speed of the walker. Find
  the speed of the cyclist and the speed of the
  walker.

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• 10) A boat takes twice as long to travel 10 km
  upstream as it does to travel 7 km downstream in
  a river that flows at a rate of 5 km/h. At what
  rate of speed does the boat travel in still water?

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• Assignment 9.5 (2 days for notes)
• 1st day assignment
• Page 582 (19-29 odd), 38, 40, 42, 44
• 2nd day assignment
• 9.5 worksheet

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Unit 9 ReviewExploring Rational Functions
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• Unit 9 Test is worth 100 points, 7 points each
• 15 questions, 2 graphing questions, 2 variation
  questions, 6 rational expression questions, 3
  rational equation questions, 2 word problems.
• Covers sections 9.1 9.5
• Study notes and hw
• Test 9 Review
• Page 586 (9-39 odd), 9.5 HW (word problems)

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• Items on the Test
• Rational Function
• Vertical Asymptote
• Horizontal Asymptote
• Discontinuity Point
• Direct Variation
• Inverse Variation
• Joint Variation
• Multiplying and Dividing Rational Expressions

• Adding and Subtracting Rational Expressions
• Solving Rational Equations and Inequalities