The problem in the image asks for the horizontal asymptote of the function $f(x) = 5^x - 4$.

To find the horizontal asymptote of this type of exponential function, we look at the behavior as $x \to \infty$ and $x \to -\infty$.

1. For $x \to \infty$, $5^x \to \infty$, so $f(x) \to \infty$.
2. For $x \to -\infty$, $5^x \to 0$, so $f(x) \to -4$.

Thus, the horizontal asymptote is $y = -4$.

The correct answer is b. $y = -4$.

Would you like further details or have any questions?

Here are 5 related questions to expand on this concept:

1. How do you find vertical asymptotes in other types of functions?
2. What happens to the graph of $f(x) = 5^x - 4$ if the constant "-4" changes to a different value?
3. How do we determine horizontal asymptotes for rational functions?
4. What is the difference between exponential growth and decay, and how does it affect the asymptote?
5. How does the base of the exponential function (in this case, 5) affect the graph?

Tip: Always consider the behavior of the function as $x \to \infty$ and $x \to -\infty$ when determining horizontal asymptotes.