To find the $y$-intercept of the function $f(x) = 8 \cos(x)$, we evaluate the function at $x = 0$ because the $y$-intercept occurs where $x = 0$.

So, $f(0) = 8 \cos(0)$

Since $\cos(0) = 1$, $f(0) = 8 \times 1 = 8$

The $y$-intercept of the graph of $f(x) = 8 \cos(x)$ is 8.

Would you like further details on this solution or have any other questions?

Further Questions:

1. What is the amplitude of the function $f(x) = 8 \cos(x)$?
2. What is the period of the function $f(x) = 8 \cos(x)$?
3. How does the graph of $f(x) = 8 \cos(x)$ compare to $g(x) = \cos(x)$?
4. What are the maximum and minimum values of $f(x) = 8 \cos(x)$?
5. What is the phase shift of the function $f(x) = 8 \cos(x)$?

Tip: To find the y-intercept of any function, substitute $x = 0$ and simplify.