It seems you've uploaded an image. Let me extract the mathematical content from it and help you with it. I'll process the image and get back to you shortly. PIL import Image

Load the uploaded image

img_path = '/mnt/data/1733659398829sre9xqam.jpg' img = Image.open(img_path)

Display the image to understand its content

img.show()I have displayed the image. I will now proceed to extract and analyze its content to assist you with the mathematics in it. pytesseract

Use pytesseract to extract text from the image

extracted_text = pytesseract.image_to_string(img)

extracted_textThe text extracted from the image suggests that the problem involves a graph of the equation $y = \frac{1}{x}$, and you're asked to find the equation of the vertical asymptote.

For the rational function $y = \frac{1}{x}$, the vertical asymptote occurs when the denominator is zero, since division by zero is undefined.

Step-by-Step Explanation:

• The function $y = \frac{1}{x}$ has a vertical asymptote where the denominator is zero. This happens when $x = 0$.
• Therefore, the vertical asymptote of the graph is at $x = 0$.

Final Answer:

The equation of the vertical asymptote is $x = 0$.

Would you like further clarification on this concept or more details on asymptotes? Here are some related questions to explore:

1. What are horizontal and oblique asymptotes, and how are they different from vertical asymptotes?
2. How do you find the asymptotes for rational functions in general?
3. What is the significance of vertical asymptotes in graphing rational functions?
4. Can a function have more than one vertical asymptote? If so, how do you find them?
5. How does the behavior of the function near the vertical asymptote differ from its behavior at other points?

Tip: Remember that vertical asymptotes occur where the denominator of a rational function equals zero, while horizontal asymptotes are determined by the behavior of the function as $x \to \infty$.