To find the horizontal asymptote(s) of the function $f(x) = \frac{2x}{x + 4}$, follow these steps:

Step 1: Analyze the degrees of the numerator and denominator.

• The degree of the numerator ($2x$) is 1.
• The degree of the denominator ($x + 4$) is 1.

Step 2: Determine the horizontal asymptote based on the degrees.

• If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is given by the ratio of the leading coefficients.

For $f(x) = \frac{2x}{x + 4}$, the leading coefficient in the numerator is 2, and the leading coefficient in the denominator is 1. Thus, the horizontal asymptote is:

$y = \frac{2}{1} = 2$

Conclusion:

The horizontal asymptote is $y = 2$.

Choice A is the correct answer:

• The horizontal asymptote(s) can be described by the line(s) $y = 2$.

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Would you like to discuss the vertical asymptotes next? Here are five related questions:

1. How do you find vertical asymptotes for rational functions?
2. What happens to $f(x)$ as $x$ approaches the vertical asymptote?
3. Can a function have both horizontal and vertical asymptotes?
4. What if the degrees of the numerator and denominator were different?
5. How do horizontal asymptotes affect the end behavior of a function?

Tip: Horizontal asymptotes represent the value that a function approaches as $x$ goes to positive or negative infinity.