The function provided is $y = 2^x - 4$.

To determine the equation of the asymptote, observe the following:

Key Insight:

For an exponential function of the form $y = a \cdot b^x + c$:

• The horizontal asymptote is given by $y = c$, where $c$ is the constant added or subtracted from the exponential part.

Applying to $y = 2^x - 4$:

• The exponential term is $2^x$.
• The constant term is $-4$, so the horizontal asymptote is $y = -4$.

Final Answer:

The equation of the asymptote is: $y = -4$

Would you like to:

1. See a detailed explanation of how the horizontal asymptote is derived?
2. Learn how to graph $y = 2^x - 4$ step-by-step?
3. Find some points to sketch the graph?
4. Explore how exponential functions behave in general?
5. Analyze other transformations of exponential functions?

Tip:

Always focus on the constant term added or subtracted to the exponential term when identifying the horizontal asymptote!