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Exponential function f(x) = ax [Home] [Search] [Forum] [Links] [Contact] [Imprint] [Sitemap]
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The precept f (x) = ax
The Graph The simplest example is: f (x) = 2x In values, that means:
That means that a number 2 to the power of an x-value makes the y-value. If the y-value is given and the x-value (is 2|4 for example), the reciprocal calculation must be used: the root! The second root (the normal one) of the x-value = 2, and x = 3, the third root, so on and so forth, from the respective y-value (in this example, it is the third root of 8 and the fourth root of 16).
Another (more difficult) example
The points 2|2 and 4|4 can be read off quite clearly. Following the precept given above, the calculations would be following.
or: The function, in which a < 1 If the base is smaller then one (but also bigger than 0), the values are similar to the values where the base is bigger than one, just the reciprocal value of it!
The Graph This is what it would look like in the coordinate system (to be exact, it is only a reflection on the y-axis):
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