The function \( f(x) = 3 \cdot \left(\frac{1}{4}\right)^{x} \) represents an exponential function.
In general, an exponential function has the form:
\[ f(x) = a \cdot b^{x} \]
where:
- \( a \) is a constant (in this case, \( a = 3 \)),
- \( b \) is the base of the exponential (in this case, \( b = \frac{1}{4} \)),
- \( x \) is the exponent.
Since \( b = \frac{1}{4} \) is between 0 and 1, this indicates that the function is a decaying exponential function.
In summary, the function \( f(x) = 3 \cdot \left(\frac{1}{4}\right)^{x} \) is an exponential decay function.