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Logarithmic Functions

Logarithmic Functions

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Logarithmic Functions

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  1. Logarithmic Functions Essential Questions • How do we write equivalent forms for exponential and logarithmic functions? • How do we write, evaluate, and graph logarithmic functions? Holt McDougal Algebra 2 Holt Algebra 2

  2. Because logarithms are the inverses of exponents, the inverse of an exponential function, such as y = 2x, is a logarithmic function, such as y = log2x. You may notice that the domain and range of each function are switched. The domain of y = 2x is all real numbers (R), and the range is {y|y > 0}. The domain of y = log2x is {x|x > 0}, and the range is all real numbers (R).

  3. Graph logarithmic functions of the form y = alogb(x – h) + k: (1, 0); (b, a) 1. Graph the 2 points: 2. Move points right/left h, up/down k. 3. Draw vertical asymptote: x = h 4. Draw curve going through 2 points.

  4. Graphing Logarithmic Functions Graph the function. State the domain and range. HA: Domain: Range: All real numbers

  5. Graphing Logarithmic Functions Graph the function. State the domain and range. HA: Left 3 Domain: Range: All real numbers

  6. Graphing Logarithmic Functions Graph the function. State the domain and range. HA: Left 2 Up 1 Domain: Range: All real numbers

  7. Graphing Logarithmic Functions Graph the function. State the domain and range. HA: Up 2 Domain: Range: All real numbers

  8. Graphing Logarithmic Functions Graph the function. State the domain and range. HA: Left 3 Down 2 Domain: Range: All real numbers

  9. Graphing Logarithmic Functions Graph the function. State the domain and range. HA: Reflect across y-axis Right 2 Up 1 Domain: Range: All real numbers

  10. Chemists regularly test samples for acidity, or concentrations of hydrogen ions (H+). Acidity is measured in pH, as given by the function:

  11. Food Application The table lists the hydrogen ion concentrations for a number of food items. Find the pH of each. 7. 8. 9.

  12. Lesson 8.3 Practice B