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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:
- 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.