Representing Real-Life Situations Using Rational Functions.pptx

Representing Real-Life Situations Using Rational Functions.pptx

• 2.
  Polynomial Function ofP of Degree in is function that can be written in form 𝑝 𝑥 = 𝑎𝑛𝑥𝑛 + 𝑎𝑛−1𝑥𝑛−1 + 𝑎𝑛−2𝑥𝑛−2 + ⋯ + 𝑎1𝑥 + 𝑎0 , where 𝑎0, 𝑎1, … , 𝑎𝑛 ∈ ℝ, 𝑎𝑛 ≠ 0, and n is a positive integer.
• 3.
  𝑝 𝑥 =𝑎𝑛𝑥𝑛 + 𝑎𝑛−1𝑥𝑛−1 + 𝑎𝑛−1𝑥𝑛−2 + ⋯ + 𝑎1𝑥 + 𝑎0
• 4.
  𝑝 𝑥 =𝑎𝑛𝑥𝑛 + 𝑎𝑛−1𝑥𝑛−1 + 𝑎𝑛−2𝑥𝑛−2 + ⋯ + 𝑎1𝑥 + 𝑎0
• 5.
  Rational function ofthe form 𝑓 𝑥 = 𝑝 𝑥 𝑞(𝑥) where 𝑝 𝑥 and 𝑞 𝑥 are polynomial functions and 𝑞 𝑥 is not the zero function ( 𝑞(𝑥) ≠ 0 ). The domain of 𝑓 𝑥 is the set of all values of x where 𝑞(𝑥) ≠ 0.
• 6.
  Representing Real-Life Situations Using RationalFunctions General Mathematics
• 7.
  At the endof the lesson, the students are expected to: a. demonstrates understanding of key concepts of rational functions; and b. accurately solve real-life problems involving rational functions
• 8.
  The local barangayreceived a budget of P100 000.00 to provide medical check-ups for the children in the barangay. The amount is to be allotted equally among all the childreninthebarangay.
• 9.
  STEP 1: Write anequation representing of the allotted amount per child (y-variable) versus the total number of children (x- variable) 𝒚 = 𝟏𝟎𝟎𝟎𝟎𝟎 𝒙
• 10.
  Fill up thetable below with different allotment for different values for the number of children. 𝒚 = 𝟏𝟎𝟎𝟎𝟎𝟎 𝒙 10 20 50 100 200 Allocated amount , y 10 000 5 000 2 000 1 000 500
• 11.
  An object isto travel a distance of 10 meters. Express velocity v(t) of travel time t, in seconds.
• 12.
  Following the tableof values below, show v for various values of t. 1 2 3 4 5 v (meters per second) 10 5 2.5 2 1
• 13.
  The function of𝐯 𝐭 = 𝟏𝟎𝟎𝟎𝟎𝟎 𝒙 can represent v as a function of t.
• 15.
  The local barangayreceived a budget of P100 000.00 to provide medical check-ups for the children in the barangay. The amount is to be allotted equally among all the children in the barangay. A philanthropist wants to supplement the budget allotted for each child by providing an additional P750 each child in thebarangay.
• 16.
  In an organpipe, the frequency f of vibration of air is inversely proportional to the length L of the pipe. Suppose that the frequency of vibration in a 10-foot-pipe is 54 vibrations per second. Express f as a functionofL.
• 17.
  The distance fromManila to Baguio is around 250 kilometers. a. How long will take you to get to Baguio if your average speed is 25 kilometers per hour? 40 kilometers perhour?50kilometers perhour? b. Construct a function (s), where s the speed of travel that describes the time it takes to drive from ManilatoBaguio
• 18.
  Suppose that 𝒄𝒕 = 𝟓𝒕 𝒕𝟐+𝟏 (in mg/mL) represents the concentration of a drug in a patient’s bloodstream t hours after the drug was administered. Construct a table of values for c(t) for t=1,2,5,10. Round your answers to three decimal places. Use the table to sketchagraphandinterprettheresults.