4.4B 2010
March 10, 2010
4.4 B Logarithmic Functions
Objective: Graph and find the domain of logarithmic functions.
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4.4B 2010
March 10, 2010
Logarithmic Functions
y = loga x if and only if x = ay
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4.4B 2010
Review:
March 10, 2010
y = 3x
x
1. Graph y = 3 .
2. Find the inverse of y = 3x.
x y
3. Graph the inverse of y = 3x.
x y
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4.4B 2010
March 10, 2010
Logarithmic Properties
f (x) = loga x 0 < a < 1
(a,1)
1) The Domain : { x | x > 0}
Range : { y | y = (All Reals)}
(1,0)
2) There are no y intercepts and the x intercept is 1.
(1/a,­1)
3) The y axis (x=0) is a vertical asymptote as x 0.
4) f(x) = loga x , 0 < a < 1, is an decreasing funtion and is one­to­one.
5) The graph of f contains the points (a,1), (1,0), (1/a,­1).
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4.4B 2010
March 10, 2010
Logarithmic Properties
f (x) = loga x
a > 1
(a,1)
(1,0)
1) The Domain : { x | x > 0}
Range : { y | y = (All Reals)}
(1/a,­1)
2) There are no y intercepts and the x intercept is 1.
3) The y axis (x=0) is a vertical asymptote as x 0.
4) f(x) = loga x , a > 1, is an increasing funtion and is one­to­one.
5) The graph of f contains the points (a,1), (1,0), (1/a,­1).
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4.4B 2010
March 10, 2010
Where did logarithm come from?
It was Exponential Funtions fault!
Logarithm is the inverse of Exponential.
y = loga (x) and y = ax for a > 1
y = loga (x) and y = ax for 0 < a < 1
Remember, logarithms and exponents are inverses.
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4.4B 2010
March 10, 2010
Use transformations to graph the function.
Determine the domain, range and vertical asymptote of the function.
1.
f(x) = 3 + log(x ­ 4)
Hint: a > 1 so the graph includes (a, 1), (1, 0) & (1/a, ­1)
D:
R:
VA:
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4.4B 2010
March 10, 2010
Use transformations to graph the function.
Determine the domain, range and vertical asymptote of the function.
2.
f(x) = 4log(x + 2)
Hint: a > 1 so the graph includes (a, 1), (1, 0) & (1/a, ­1)
D:
R:
VA:
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4.4B 2010
March 10, 2010
Use transformations to graph the function.
Determine the domain, range and vertical asymptote of the function.
3.
f(x) = 3 + ln(x)
Hint: a > 1 so the graph includes (a, 1), (1, 0) & (1/a, ­1)
D:
R:
VA:
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4.4B 2010
March 10, 2010
Homework:
page 296
#'s: 42 ­ 45, 57 ­ 60, 67 ­ 74, 76, 77, 84, 85, 91­102
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4.4B 2010
March 10, 2010
When are logarithms used today?
The decible is the unit of volume from a speaker!
We all love our i­pods and music the decible system is based on Logarithums!!
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