ANSWER
An exponential growth function.
Step-by-step explanation
The given function is
![f(x) = (1)/(2) {(3})^(x)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/o14f3tf0vd3hm1rtfcinn0up0zbaf6o0q4.png)
This function is of the form,
![f(x) = a {(b})^(kx)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/yz193pji7sgp0z19v9ld6kh3glp0okaph4.png)
Since k is positive , the function will grow exponentially and fall asymptote to the negative x-axis.
As x-values becomes bigger and bigger positively, the graph grows exponentially.