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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.

Consider the given equation: f(x) = (1/4) * (1/8)^x. The y-intercept is ___

Learn how to find the y-intercept of the exponential function f(x) = (1/4) * (1/8)^x. This problem demonstrates key concepts in exponential functions and intercepts. Suitable for students in Grades 9-12.

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