https://file.aiquickdraw.com/mathbot/file/17371405221954q8mulbi.jpg

The equation provided is:

\[
y = \frac{4}{x}
\]

This is a **rational function**. To graph it, we need to select points for \(x\), calculate the corresponding \(y\)-values, and plot those points. Let’s choose values for \(x\), calculate \(y\), and plot at least two points on each side of the \(y\)-axis.

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### Step 1: Choose values for \(x\) and calculate \(y\):
1. \(x = 1\): \(y = \frac{4}{1} = 4\)
2. \(x = 2\): \(y = \frac{4}{2} = 2\)
3. \(x = -1\): \(y = \frac{4}{-1} = -4\)
4. \(x = -2\): \(y = \frac{4}{-2} = -2\)

### Step 2: Points to plot
- For \(x > 0\): \((1, 4)\) and \((2, 2)\)
- For \(x < 0\): \((-1, -4)\) and \((-2, -2)\)

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### Step 3: Characteristics of the Graph
- The graph has **vertical asymptote** at \(x = 0\) (since division by zero is undefined).
- The graph also has a **horizontal asymptote** at \(y = 0\) (as \(x\) becomes very large or very small, \(y\) approaches 0).

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Would you like me to provide further details or additional help with graphing?  

### Related Questions:
1. What are the properties of rational functions?
2. How can we find the domain of \(y = \frac{4}{x}\)?
3. What do vertical and horizontal asymptotes represent?
4. How do rational functions differ from polynomial functions?
5. How would the graph of \(y = \frac{-4}{x}\) compare to this one?

**Tip:** Always calculate points on both sides of key asymptotes for a clearer understanding of the graph!

Graph the equation y = 4/x by plotting points. Plot at least two points on each side of the y-axis.

Learn how to graph the rational function y = 4/x by plotting points. Explore the properties of rational functions, vertical and horizontal asymptotes, and how to analyze the graph for key behaviors. This problem is ideal for students in Grades 8-10.

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