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Graphing logarithmic and exponential functions

Graph of logarithmic functions

  • Graphing logarithmic functions follows the same rules as graphing other functions. For example if we were to graph \(y=\log(x)\) we would need to remember that logarithms are not defined for negative values of \(x\) or for \(x=0\). That is the domain is \(x>0\).

  • Firstly, draw up a table of values:
 \(x\)  \(0.01\)  \(0.1\)  \(1\)  \(10\)  \(100\)
 \( y = \log_{10}(x) \) \(-2\) \(-1\) \(0\) \(1\)  \(2\)

  • Secondly, plot the points:

Logarithmic Graph

  • Simple Logarithmic graphs all have similar shapes to the figure above.
  • The domain is restricted and includes only real numbers greater than zero (you cannot find a logarithm of a negative number).
  • There will be an \(x\)-intercept, in this case \(x=1\).
  • As the independent variable decreases (approaches zero) the dependent variable approaches negative infinity.
  • As the independent variable increases (approaches infinity, \(\infty\)) the dependent variable increases slowly.

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