To determine the characteristics of the exponential function \( g(x) = e^x \), we can draw from the properties of logarithmic and exponential functions.
-
Domain of \( g(x) \):
The exponential function \( g(x) = e^x \) is defined for all real numbers. Therefore, the domain of \( g(x) \) is \( x \in (-\infty, \infty) \). -
Range of \( g(x) \):
The output of the exponential function \( e^x \) is always positive as \( e^x > 0 \) for all real \( x \). Thus, the range of \( g(x) \) is \( y > 0 \).
Given the above points, the correct statement about the corresponding exponential function \( g(x) \) is:
Function \( g(x) \) has a range of \( y > 0 \).
Hence, the correct response is:
Function g(x) has a range of y>0.