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The function provided in the image is \( h(x) = \frac{1}{x - 3} \), and you're asked to determine its domain.

### Domain of the function:
The domain of a function consists of all the values of \( x \) for which the function is defined. For a rational function like this, it is undefined when the denominator is zero because division by zero is not possible.

In this case, the denominator is \( x - 3 \). To find when this is zero:
\[
x - 3 = 0 \implies x = 3
\]
Thus, the function is undefined at \( x = 3 \).

### Conclusion:
The domain of \( h(x) = \frac{1}{x - 3} \) is all real numbers except \( x = 3 \).

### In interval notation, the domain is:
\[
(-\infty, 3) \cup (3, \infty)
\]

Would you like further clarification or details?

Here are 5 related questions to explore this further:
1. What is the range of the function \( h(x) = \frac{1}{x - 3} \)?
2. How do vertical asymptotes relate to the domain of a rational function?
3. Can you find the domain of a function with a square root in the denominator?
4. What happens to \( h(x) \) as \( x \) approaches 3?
5. How do you determine the domain for a function with multiple variables?

**Tip:** Always check for points where the denominator of a rational function becomes zero to determine where it is undefined.

For the function h(x) = 1/(x - 3), determine the domain.

Learn how to determine the domain of the rational function h(x) = 1/(x - 3). This problem explains the concept of undefined points in rational functions, focusing on division by zero. Suitable for high school students.

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