Draw the graph of y = 1 / x².

To graph the function \( y = \frac{1}{x^2} \), follow these steps:

Understanding the Function

This function is defined for all real numbers except \( x = 0 \). As \( x \) approaches zero, \( y \) increases rapidly towards infinity. For positive and negative values of \( x \), \( y \) is always positive.

Key Features of the Graph

• Asymptotes: The graph has a vertical asymptote at \( x = 0 \) and a horizontal asymptote at \( y = 0 \).
• Shape: The graph is a curve that approaches the axes but never touches them.
• Symmetry: The graph is symmetric with respect to the y-axis.

Plotting Points

To create the graph, plot several points:

• For \( x = 1 \), \( y = 1 \)
• For \( x = 2 \), \( y = 0.25 \)
• For \( x = -1 \), \( y = 1 \)
• For \( x = -2 \), \( y = 0.25 \)

Sketching the Graph

Using the points plotted, draw a smooth curve that approaches the axes without touching them. The graph will look like two separate curves in the first and second quadrants.

Final Thoughts

This graph visually represents how \( y \) behaves as \( x \) changes, illustrating the concept of inverse square relationships effectively.