Grade 11 Mathematics Power Polynomial and Rational Functions
- Slides: 27
Grade 11 Mathematics Power, Polynomial, and Rational Functions ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation
The graph of y = 1/x PA 1. 5 You should also be familiar with the graph of Notice that the curve gets closer and closer to the x- and y-axes but never touches them. y 0 This is a reciprocal function . x The x- and y-axes form asymptotes. The graph of is an example of a discontinuous function. ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation
PA 1. 5 Graphs of the form y = kx–n ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation
PA 1. 5 Reciprocal functions A reciprocal function always contains a fraction with a term in x in the denominator. Here are examples of three simple reciprocal functions: y = – 4 y= 3 y= 1 x x x In each of these examples the axes form asymptotes. The curve never touches these lines. ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation
PA 1. 5 Exploring reciprocal graphs ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation
PA 1. 5 Translating reciprocal functions vertically ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation
PA 1. 5 Translating reciprocal functions horizontally ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation
PA 1. 5 Stretching reciprocal functions vertically ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation
PA 1. 5 Stretching reciprocal functions horizontally ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation
PA 1. 5 ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation
PA 1. 5 ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation
PA 1. 5 ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation
PA 1. 5 ﺍﻟﺮﻳﺎﺿﻴﺎﺕ – ﺗﻔﻜﻴﺮ ﺳﻠﻴﻢ – ﺩﻗﺔ ﻭﺗﻌﺎﻭﻥ – ﺻﺒﺮ ﻭﻧﻈﺎﻡ – ﺗﺬﻭﻕ ﺍﻟﺠﻤﺎﻝ ﺍﻟﻌﻠﻤﻲ. Mathematics- Proper Thinking- Accuracy and Cooperation- Patience and Discipline- Science Beauty sensation
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