how to get the domain and range of an exponential function? g(x)=10^x
Domain = All values of x from neg.
infinity to pos. infinity.
To find the domain and range of an exponential function, such as g(x) = 10^x, you need to understand the properties of exponential functions.
The domain refers to all possible input values for the function, while the range represents all possible output values.
1. Domain:
In the case of exponential functions, the domain is typically all real numbers, since the variable "x" can take any arbitrary value. Therefore, the domain of g(x) = 10^x is (-∞, +∞), indicating that there are no restrictions on the input values.
2. Range:
To determine the range, you can examine the behavior of the exponential function. In this case, the function g(x) = 10^x represents exponential growth because the base (10) is greater than 1.
For exponential growth functions, the range is always positive, as the output values increase with increasing input values. Therefore, the range of g(x) = 10^x is (0, +∞), which means the function can produce any positive number, but it cannot reach zero or negative values.
Remember, these rules apply to most exponential functions, but there are exceptions as well. Always consider the specific properties and restrictions of the function being analyzed to determine the accurate domain and range.