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

Step 1: Identify potential vertical asymptotes.

• Vertical asymptotes occur where the denominator of a rational function is equal to zero (and the numerator is non-zero at that point).

Step 2: Set the denominator equal to zero.

• The denominator of $f(x) = \frac{2x}{x + 4}$ is $x + 4$.

Set the denominator equal to zero and solve for $x$: $x + 4 = 0$ $x = -4$

Conclusion:

• There is a vertical asymptote at $x = -4$.

Choice A is the correct answer:

• The vertical asymptote(s) can be described by the line $x = -4$.

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Would you like further details on this, or do you have any other questions? Here are five related questions:

1. What happens to $f(x)$ as $x$ approaches $-4$ from the left and right?
2. Can a function have more than one vertical asymptote?
3. How does the presence of vertical asymptotes affect the graph of a function?
4. What is the difference between a vertical asymptote and a hole in the graph?
5. How do you determine if a vertical asymptote exists using limits?

Tip: Vertical asymptotes represent values of $x$ where the function becomes undefined and the function value tends to $\pm \infty$.