range of exponential function
The range of an exponential function depends on the type of exponential function and the domain you are considering
The range of an exponential function depends on the type of exponential function and the domain you are considering.
For the basic exponential function, y = a^x, where a is a positive constant and x can be any real number, the range will depend on the sign of the base.
If a > 1, then the exponential function will have a range of (0, ∞), meaning that the output values (y) will be positive and can approach infinity but will never reach zero. This is because as x approaches negative infinity, a^x approaches 0, and as x approaches positive infinity, a^x approaches infinity.
If 0 < a < 1, then the range of the function will be (0, 1), meaning that the output values will be positive but less than 1. As x approaches negative infinity, a^x approaches infinity, and as x approaches positive infinity, a^x approaches 0. If a = 1, then the output values will always be 1, so the range of the function is just {1}. If a ≤ 0 or a is a negative number, then the function is not defined for real values of x, and therefore has no range. It's important to note that these ranges are for the basic exponential function. If the exponential function is transformed by shifting, stretching, or reflecting, the range may change accordingly.
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