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Graphing logarithmic and exponential functions

Exponential graphs

As with graphing other functions, follow the same rules:

  • Select a relevant domain.
  • Draw up the table of values.
  • Plot the points.

For example, plot the curve \(y=2^x\):

 \(x\) \( -3\) \( -2\)  \(-1\)  \(\ 0\ \)  \(\ 1\ \)  \(\ 2\ \) \(\ 3\ \)
 \(y = 2^x \)  \(0.125\)  \(0.25\)  \(0.5\) \( 1\)  \(2\)  \(4\) \( 8\)

  • Simple exponential growth graphs all have the same shape as the figure above.
  • The range includes only real numbers greater than zero.
  • There will be a \(y\)-intercept, in this case \(y=1\).
  • As the independent variable decreases (approaches negative infinity, \( -\infty \)) the dependent variable approaches zero.
  • As the independent variable increases (approaches infinity) the dependent variable increases rapidly.