Today in Precalculus•Go over homework•Notes: Log Functions(need a

calculator)–Graphing–Applications

•Homework

Extrema:

Asymptotes:

D: ( 0,∞)

R: ( – ∞, ∞ )

x-int: (1, 0)

continuous

incr: ( 0, ∞)

no symmetry

unbounded

D:

R:intercepts

continuity

Incr. / decr.

Symmetry

Boundedness

Extrema: none

Asymptotes: x = 0End Behavior:

Graphing Log Functions

y = e^xy = ln(x)

y = 10^xy = log(x)

TransformationsDescribe 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-axisshift up 2

original points: (1,0) & (2.7,1)

TransformationsDescribe 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-axisreflect over x-axisvertical stretch 2shift up 1

original points: (1,0) & (10,1)

Applicationsf(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

Application

t f(t)0 756 63.310 60.6

Sound Intensity• A log model used for measuring the intensity

of sound.0

10log II

I: intensityI0 =10-12 watts per square meter

is the level of sound in decibels

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

0

10log II

8

12

1010log10

410log10 10(4)

40 decibels

Homework

• Page 308: 41-44, 47, 49, 50, 59, 60• Quiz: Friday, December 18