ANSWER
An exponential growth function.
EXPLANATION
The given function is
[tex]f(x) = \frac{1}{2} {(3})^{x} [/tex]
This function is of the form,
[tex]f(x) = a {(b})^{kx} [/tex]
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.
