The graph in the image shows a transformation of the function $y = 2^x$. Upon observing the graph, it appears to be flipped vertically and shifted downward. Let’s analyze the transformation step-by-step:

1. Vertical Reflection: The graph is flipped across the x-axis, indicating a vertical reflection. This is achieved by multiplying the function by $-1$. $y = -2^x$

2. Vertical Shift: The entire graph is shifted downward by 4 units. This is achieved by subtracting 4 from the function: $y = -2^x - 4$

Thus, the equation for the graph is: $y = -2^x - 4$

Would you like further clarification or additional examples?

Here are 5 follow-up questions related to this topic:

1. What transformations occur if the graph is shifted upward by 3 units instead?
2. How does a horizontal shift affect the equation of an exponential function?
3. Can you explain why multiplying by $-1$ reflects the graph over the x-axis?
4. What happens to the function if $y = 2^x$ is stretched vertically by a factor of 3?
5. How would you write the equation if the graph were shifted both horizontally and vertically?

Tip: Always analyze transformations in the order: reflections, stretches/compressions, and then shifts.