To find the y-intercept of the function \( f(x) = \left(\frac{1}{4}\right)^x \), we need to evaluate \( f(0) \), since the y-intercept occurs where \( x = 0 \).
Calculating \( f(0) \):
\[ f(0) = \left(\frac{1}{4}\right)^0 = 1 \]
So the y-intercept is \( (0, 1) \).
The correct answer is: A. (0, 1)