Find the vertical asymptote of the graph of the function.

​f(x)equals=StartFraction 1 Over left parenthesis x minus 1 right parenthesis squared EndFraction

The function given is:

\[
f(x) = \frac{1}{(x - 1)^2}
\]

To find the vertical asymptote, we need to determine where the denominator of the function becomes zero because a vertical asymptote occurs when the function tends to infinity due to division by zero.

The denominator is \((x - 1)^2\). Set the denominator equal to zero:

\[
(x - 1)^2 = 0
\]

Solve for \(x\):

\[
x - 1 = 0 \quad \Rightarrow \quad x = 1
\]

Therefore, the vertical asymptote of the function is at:

\[
x = 1
\]

Would you like more details or have any questions?

Here are five related questions:
1. What is the behavior of the function near the vertical asymptote \(x = 1\)?
2. How would the graph of the function look near the asymptote?
3. Are there any horizontal asymptotes in this function?
4. How does the exponent of \((x - 1)^2\) affect the type of asymptote?
5. What happens to the function as \(x\) approaches positive and negative infinity?

**Tip:** To find vertical asymptotes, always focus on when the denominator equals zero while ensuring the numerator is non-zero at those points.

Find the vertical asymptote of the graph of the function f(x) = 1 / (x - 1)^2.

Learn how to find the vertical asymptote of the function f(x) = 1 / (x - 1)^2. This problem covers key calculus concepts such as limits and asymptotes. Suitable for students in Grades 10-12.

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