Question

Identify the horizontal asymptote of f(x) = 4 x over 7.

y = 0
y = 4 over 7
y = 7 over 4
No horizontal asymptote

Answer 1

To determine the horizontal asymptote of the function \( f(x) = \frac{4x}{7} \), we can analyze the behavior of the function as \( x \) approaches infinity (\( x \to \infty \)) or negative infinity (\( x \to -\infty \)).

1. As \( x \) approaches infinity:
\[
f(x) = \frac{4x}{7}
\]
In this case, the function approaches infinity as well, and there is no horizontal asymptote.

2. As \( x \) approaches negative infinity:
\[
f(x) = \frac{4x}{7}
\]
Similarly, this also approaches negative infinity.

Since the function behaves linearly (increasing or decreasing without bound) as \( x \) approaches both positive and negative infinity, we conclude that there is no horizontal asymptote.

So, the correct answer is:
**No horizontal asymptote**.