Today in Precalculus

1. Today in Precalculus • Go over homework • Notes: Log Functions(need a calculator) • Graphing • Applications • Homework

2. Graphing Log Functions continuity D: ( 0,∞) continuous D: Extrema: none Extrema: Incr. / decr. R: ( – ∞, ∞ ) incr: ( 0, ∞) R: Asymptotes: Asymptotes: x = 0 End Behavior: intercepts Symmetry x-int: (1, 0) no symmetry

3. Transformations Describe how to transform the graph of the f(x) = ln x into the graph of the given function. Sketch by hand. a.) g(x) = ln (– x) + 2 reflect over y-axis shift up 2 original points: (1,0) & (2.7,1)

4. Transformations Describe how to transform the graph of the f(x) = log x into the graph of the given function. Sketch by hand. b.) h(x) = -2 log(-x) +1 reflect over y-axis reflect over x-axis vertical stretch 2 shift up 1 original points: (1,0) & (10,1)

5. Applications f(t) = 75 – 6ln(t + 1) for 0 ≤ t ≤ 12 where t is time in months • What was the average score on the original exam (t = 0)? f(0) = 75 – 6ln(0+1) = 75 – 6(0) = 75 • After six months, what was the average score? f(6) = 75 – 6ln(6+1) = 63.325 • After ten months, what was the average score? f(10) = 75 – 6ln(10+1) = 60.613

6. Application

7. Sound Intensity • A log model used for measuring the intensity of sound. I: intensity I0 =10-12 watts per square meter

8. Example • Find the level of sound if the intensity is 10-8

9. Homework • Page 308: 41-44, 47, 49, 50, 59, 60 • Quiz: Thursday, December 8