Here's the graph of the function $y = \sec(-x - \frac{\pi}{4}) - 3$, showing the reflection, left shift, and vertical translation.

Let me know if you'd like further details or have any questions about the graph!

Related Questions:

1. How do shifts and reflections affect the graph of a secant function?
2. How do you determine the locations of the vertical asymptotes for a secant function?
3. What is the relationship between the cosine and secant functions?
4. How do transformations of the argument in the secant function change its graph?
5. How can you identify key points and behavior in trigonometric graphs?

Tip: When graphing trigonometric functions like secant or cosine, focus on finding the asymptotes first, as they guide where the graph will approach infinity.