Exponential functions > Exponential functions
12345Exponential functions

Theory

Take a look at the applet: Exponential Function

The graph of the exponential function f ( x ) = b g x has the following characteristics:

  • The graph intersects the y -axis at the point ( 0 , b ) .

  • If b > 0 and g > 1 the graph is increasing. To the left (for decreasing x ) the graph approaches the x -axis. You can take the function value as close to 0 as you like by taking x sufficiently small. The x -axis is the horizontal asymptote.

  • If b > 0 and 0 < g < 1 the graph is decreasing. To the right (for increasing x ) the graph approaches the x -axis, the horizontal asymptote.

  • If b < 0 and 0 < g < 1 the graph is increasing. To the right (for increasing x ) the graph approaches the x -axis, the horizontal asymptote.

  • If b < 0 and g > 1 the graph is decreasing. To the left (for decreasing x ) the graph approaches the x -axis, the horizontal asymptote.

  • If g = 1 the graph is the horizontal line y = b .

Exponential equations like b g x = a can be solved using the calculator.

For exponential inequalities one uses the properties mentioned above .

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