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The question in the image asks:

**Q1. At what points are functions continuous?**
Given function:
\[
y = \frac{1}{x-2} - 3x
\]

### To determine the continuity of the function:

1. The function is the sum of two parts: \(\frac{1}{x-2}\) and \(-3x\).
   - The term \(-3x\) is a polynomial, and polynomials are continuous everywhere in the real number system.
   - The term \(\frac{1}{x-2}\) is a rational function, which is continuous everywhere except where the denominator is zero.

2. The denominator of the rational term \(\frac{1}{x-2}\) is zero when \(x = 2\). At this point, the function is undefined, so the function is **discontinuous at \(x = 2\)**.

### Conclusion:
- The function \( y = \frac{1}{x-2} - 3x \) is continuous for all real numbers **except** at \(x = 2\), where it has a discontinuity.

Would you like more details on the nature of this discontinuity or further clarification?

### Related questions:
1. What is the definition of a continuous function at a point?
2. How do you identify discontinuities in a rational function?
3. What types of discontinuities exist in functions?
4. Can a function be made continuous at a discontinuity? If so, how?
5. How does the behavior of a function near a discontinuity affect its limit?

### Tip:
When examining rational functions, always check where the denominator equals zero, as this typically indicates points of discontinuity.

At what points are functions continuous?
Given function: y = 1/(x - 2) - 3x

Explore the continuity of the rational function y = 1/(x-2) - 3x. Learn how to determine the points where the function is continuous, identify discontinuities in rational functions, and understand the behavior of the function near x = 2.

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