Natural Logarithmic Function Graphs
(single transformations)

Desmos File: Log base e 
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  • this is the parent function of logarithmic functions
  • x = 0 is the vertical asymptote of this function
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Desmos File: a log base e
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  • this is a vertical dilation of the parent logarithmic function
  • x = 0 is the vertical asymptote of this function  

Desmos File:
y= log base e (cx)
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  • ​this is a horizontal dilation of the parent logarithmic function
  • x = 0 is the vertical asymptote of this function

Desmos File:
y= log base e (x+d)
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  • ​this is a horizontal shift of the parent logarithmic function
  • x = -d is the vertical asymptote of this logarithmic function

Desmos File:
y= log base e (x)+f
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  • this is a vertical shift of this logarithmic function
  • x = 0 is the vertical asymptote of this logarithmic function