To find the **x-intercept** of the function \( y = x - \frac{1}{x} \), we need to set \( y = 0 \) and solve for \( x \).

So, solve:

\[
0 = x - \frac{1}{x}
\]

Multiply through by \( x \) to eliminate the fraction:

\[
0 = x^2 - 1
\]

This simplifies to:

\[
x^2 = 1
\]

Taking the square root of both sides:

\[
x = \pm 1
\]

Thus, the x-intercepts are \( x = 1 \) and \( x = -1 \).

### Summary:
The x-intercepts are at \( x = 1 \) and \( x = -1 \).

Would you like further details or have any questions?

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Here are five related questions for further practice:

1. What is the y-intercept of the function \( y = x - \frac{1}{x} \)?
2. How would you find the critical points of this function?
3. What is the behavior of the function as \( x \to \infty \)?
4. Can you sketch the graph of the function \( y = x - \frac{1}{x} \)?
5. How do you determine the asymptotes for this function?

**Tip:** When solving rational equations, multiplying through by a common denominator helps eliminate fractions.

Learn how to find the x-intercepts of the function y = x - 1/x. This step-by-step solution involves setting y to 0 and solving the rational equation. Key concepts include intercepts, rational functions, and algebraic simplification. Suitable for students in Grades 9-12.

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