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Main Ideas of Adv PreCalc Ch. 3 Class 1

Main Ideas of Adv PreCalc Ch. 3 Class 1. Exponential Function Graphs of f(x) = a x Growth if a > 1 Decay if 0 < a < 1 Graph key points: x = -1, 0, 1 Properties of Exponents Multiply: add exponents Divide: subtract exponents Power to a power: multiply exponents Translation of Graphs

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Main Ideas of Adv PreCalc Ch. 3 Class 1

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  1. Main Ideas of AdvPreCalc Ch. 3 Class 1 Exponential Function Graphs of f(x) = ax Growth if a > 1 Decay if 0 < a < 1 Graph key points: x = -1, 0, 1 Properties of Exponents Multiply: add exponents Divide: subtract exponents Power to a power: multiply exponents Translation of Graphs f(x-h) translates to right h units f(x) + k translates graph up k units f(-x) reflects graph in the y-axis -f(x) reflects in the y-axis Natural Base e Compound Interest

  2. Main Ideas of AdvPreCalc Ch. 3 Class 2 Logarithmic Function Logs are Exponents! y = log ax iff x = ay Properties of logs loga 1 = 0 loga a = 1 loga ax = x alogax = x loga x= logayiff x = y Graphs of f(x) = loga x Translation of Graphs f(x-h) translates to right h units f(x) + k translates graph up k units f(-x) reflects graph in the y-axis -f(x) reflects in the y-axis Natural Base e Domain of Exponential and Log Functions

  3. Main Ideas of AdvPreCalc Ch. 3 Class 3 Properties of Logarithms Logs are Exponents! Change of Base Product property Add Logs Quotient Property Subtract Logs Power Property Multiply Logs Expanding Logs Condensing Logs

  4. Main Ideas of AdvPreCalc Ch. 3 Class 4 Solving Exponential Equations Isolate the exponential term Use the inverse property of the logs and exponentials: take log of both sides Solving Logarithmic Equations Isolate the logarithmic term Use the inverse property of logs and exponentials: exponentiate each side

  5. Main Ideas of AdvPreCalc Ch. 3 Class 5 Applications or Exponentials and Logarithmic Functions Population Growth Logistic Growth Population Growth with Limitations Spread of Disease Radioactive Decay Estimating fossil dates Richter Scale Modeling Linear Quadratic Exponential Logarithmic

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