To determine whether the function [tex]\( f(x) = 3^x \)[/tex] is an exponential function, we need to recall the definition of an exponential function.
An exponential function is a function of the form [tex]\( f(x) = a^x \)[/tex], where:
- [tex]\( a \)[/tex] is a constant,
- [tex]\( a > 0 \)[/tex],
- [tex]\( a \neq 1 \)[/tex],
- [tex]\( x \)[/tex] is a variable.
Let's analyze the given function step-by-step:
1. Identify the base [tex]\( a \)[/tex]: For the function [tex]\( f(x) = 3^x \)[/tex], the base [tex]\( a \)[/tex] is 3.
2. Check if [tex]\( a > 0 \)[/tex]: Here, [tex]\( a = 3 \)[/tex], and 3 is clearly greater than 0.
3. Check if [tex]\( a \neq 1 \)[/tex]: Here, [tex]\( a = 3 \)[/tex], and 3 is not equal to 1.
Given that all conditions for [tex]\( a \)[/tex] (i.e., being a positive constant different from 1) are satisfied, the function [tex]\( f(x) = 3^x \)[/tex] fits the definition of an exponential function.
Therefore, the statement that the function [tex]\( f(x) = 3^x \)[/tex] is an exponential function is True.
