Range of the Exponential Function
The range of a function y = f(x) is the set of all the functions' values when x moves through its domain.
It's required to find the range of the function:
![y=6^x^{}](https://img.qammunity.org/2023/formulas/mathematics/college/iwrwhhqfgnlmzha5prmzrn4ubx1ki0f5mv.png)
The domain of the function is the set of all the real numbers because x can be given any possible value and y would still exist.
For example, let's give x the values x={-3,-1,0,2,4}
![f(-3)=6^(-3)=0.005](https://img.qammunity.org/2023/formulas/mathematics/college/73vlxme64yo6q3r9rce806a4sbdph59v5a.png)
![f(-1)=6^(-1)=0.167](https://img.qammunity.org/2023/formulas/mathematics/college/9hx8n3h3nm1xqrashd667ianr90wgapd7b.png)
![f(0)=6^0=1](https://img.qammunity.org/2023/formulas/mathematics/college/w6iqopy94a11tdk1cd8kpamisfehh5t406.png)
![\begin{gathered} f(2)=6^2=36 \\ f(4)=6^4=1296 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/q3l3ymiwyqe51sj6084f8npt83h06niloj.png)
It's clear that for negative values of x, the function tends to zero and for positive values, the function tends to infinity.
Thus, the range of the function is (0,