The given equation is:

$f(x) = \frac{1}{4} \cdot \left( \frac{1}{8} \right)^x$

To find the y-intercept:

The y-intercept occurs when $x = 0$. Let's substitute $x = 0$ into the equation:

$f(0) = \frac{1}{4} \cdot \left( \frac{1}{8} \right)^0$

Since any number raised to the power of 0 is 1, this simplifies to:

$f(0) = \frac{1}{4} \cdot 1 = \frac{1}{4}$

So, the y-intercept is $\frac{1}{4}$.

Summary:

The y-intercept is $\frac{1}{4}$.

Would you like more details or have any questions on this? Here are some related questions to further explore the concept:

1. What is the general form of an exponential function?
2. How does changing the base of the exponent affect the graph?
3. What is the x-intercept of this function?
4. How can you graph this function manually?
5. How does this function behave as $x$ increases or decreases?

Tip: For exponential functions, the y-intercept is always the value of the function when $x = 0$, which is a quick way to find it.