Find the vertical asymptotes. Select the correct choice below and fill in any answer boxes within your choice.

A.

The vertical​ asymptote(s) can be described by the​ line(s) 

enter your response here.

​(Type an equation. Use a comma to separate answers as​ needed.)

B.

There are no vertical asymptotes.

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 \( \pm \infty \).

Learn how to find the vertical asymptotes of the function f(x) = 2x/(x + 4) with a step-by-step solution. Understand where vertical asymptotes occur in rational functions and how to determine them algebraically. Suitable for high school students studying functions and rational expressions.

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