GraphsofLogarithmicFunctions
Review: Find the inverse of f ( x ) 
Find the inverse of f ( x)  2
x2
3
x
The exponential function has an inverse called _______________________
Definition of Logarithmic Function:
b  1 , b y  x is equivalent to y  log b x
The function f ( x)  logb x is the logarithmic function with base b.
For x  0 and b  0,
Graph the following Inverse Functions:
f ( x)  2 x
f ( x)  log 2 x
Domain:___________________
Domain:___________________
Range:____________________
Range:____________________
X-int:_____________________
X-int:_____________________
Y-Int:_____________________
Y-Int:_____________________
Asymptote:________________
Asymptote:________________
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Graph the following Inverse Functions:
f ( x)  4 x
f ( x)  log 4 x
Domain:___________________
Domain:___________________
Range:____________________
Range:____________________
x-int:_____________________
x-int:_____________________
y-int:_____________________
y-int:_____________________
Asymptote:________________
Asymptote:________________
Note: Some bases are used frequently, and have simplified notation.
Common Log (Base 10): log10 x =
Natural Log (Base e): log e x =
Inverse Functions
Logarithm Form
Exponential Form
f ( x)  b x
f ( x )  10 x
f ( x)  e x
Transformations:
Parent Function: f  x   log b x All logarithmic functions (in “basic” form) have 2 points on their
graphs: (1,0) and (b,1)
Vertical Shift
f  x   log b x  c
f  x   log b x  c
Horizontal Shift
f  x   log b  x  c 
f  x   log b  x  c 
Reflections
f  x    log b x
Vertical Stretch and
Compress
f  x   c log b x
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Sketch f ( x)  log x
Then, sketch the following
f ( x)  log x  2
f ( x )  log( x  2)
f ( x )  log( x  1)  4
f ( x)  2log x
f ( x)   log( x  2)  3
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Sketch f ( x)  ln x
Then, sketch the following
f ( x)  ln  x  3
f ( x )  ln x  3
f ( x )  ln( x  2)  4
f ( x)  1 ln x
2
f ( x)   ln( x  1)  2
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