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

Finding the Horizontal Asymptote

For exponential functions of the form $f(x) = a^x + c$, the horizontal asymptote is given by the constant term $c$ because as $x \to -\infty$, the term $a^x$ approaches zero.

In this case, the function is $f(x) = 5^x - 4$, where $a = 5$ and $c = -4$. As $x \to -\infty$, $5^x$ approaches 0, and the function tends toward $f(x) \to -4$.

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

Answer:

The correct choice is: b. $y = -4$

Let me know if you want more details or explanations! Here are some follow-up questions to deepen your understanding:

1. What is the horizontal asymptote of the function $f(x) = 2^x + 3$?
2. How do you find vertical asymptotes for rational functions?
3. What happens to $5^x$ as $x \to \infty$?
4. Can an exponential function have more than one horizontal asymptote?
5. How does shifting an exponential graph vertically affect its asymptote?

Tip: For exponential functions, the horizontal asymptote always depends on the vertical shift applied to the base function $a^x$.