range of exponential function
The range of an exponential function depends on whether it is an increasing or decreasing function and the values of its parameters
The range of an exponential function depends on whether it is an increasing or decreasing function and the values of its parameters.
For an exponential function of the form f(x) = a * b^x, where a and b are constants and b is positive, we have two cases:
1. If the base (b) of the exponential function is greater than 1, then the function is increasing. In this case, the range is (0, +∞), meaning the function takes on all positive real values. This is because as x approaches positive infinity, the exponential term grows without bound.
2. If the base (b) of the exponential function is between 0 and 1, then the function is decreasing. In this case, the range is (0, a], where a is the initial value of the function (the value when x is equal to zero). The range includes zero and all values less than or equal to a. This is because as x approaches positive infinity, the exponential term approaches zero, resulting in values approaching a (the initial value).
It’s important to note that if the exponential function includes restrictions or transformations (such as translations or reflections), these can affect the range. Make sure to take these into account when determining the range of a specific exponential function.
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