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

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

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

5. Holt McDougal Algebra 2 Logarithmic Functions Graphing Logarithmic Functions Graph the function. State the domain and range. Domain: All real numbers Range: xy HA:

6. Holt McDougal Algebra 2 Logarithmic Functions Graphing Logarithmic Functions Graph the function. State the domain and range. Domain: All real numbers Range: xy HA: Left 3

7. Holt McDougal Algebra 2 Logarithmic Functions Graphing Logarithmic Functions Graph the function. State the domain and range. Domain: All real numbers Range: xy HA: Left 2 Up 1

8. Holt McDougal Algebra 2 Logarithmic Functions Graphing Logarithmic Functions Graph the function. State the domain and range. Domain: All real numbers Range: xy HA: Up 2

9. Holt McDougal Algebra 2 Logarithmic Functions Graphing Logarithmic Functions Graph the function. State the domain and range. Domain: All real numbers Range: xy HA: Left 3 Down 2

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

11. Holt McDougal Algebra 2 Logarithmic Functions Chemists regularly test samples for acidity, or concentrations of hydrogen ions (H + ). Acidity is measured in pH, as given by the function:

12. Holt McDougal Algebra 2 Logarithmic Functions The table lists the hydrogen ion concentrations for a number of food items. Find the pH of each. Food Application SubstanceH + conc. (mol/L) Milk 0.00000025 Tomatoes 0.0000316 Lemon juice 0.0063 7. 8. 9.

13. Holt McDougal Algebra 2 Logarithmic Functions Lesson 8.3 Practice B