It looks like you've uploaded an image with a question related to the behavior of a function as $x$ approaches 1. Based on the mathematical expression $y = \frac{x^3 - 2x^2 + 1}{(x - 1)^3}$, the function behaves differently near $x = 1$.

Let's break this down:

• For values of $x$ less than 1, the denominator of the function is $(x - 1)^3$, which is negative (since $x - 1 < 0$), so the value of the function becomes negative and its magnitude increases as $x$ approaches 1.

• For values of $x$ greater than 1, the denominator $(x - 1)^3$ is positive (since $x - 1 > 0$), so the function value becomes positive and increases as $x$ approaches 1.

To fill in the blanks:

1. For values of $x$ less than 1, the denominator is negative, so the value of the function goes to negative infinity.
2. For values of $x$ greater than 1, the denominator is positive, so the value of the function goes to positive infinity.
3. For values of $x$ near 1, the denominator becomes very small (close to 0), making the function approach infinity in magnitude.

Would you like me to go into more details on this or clarify any part of the explanation?

Here are five related questions:

1. What happens to the function if we approach $x = 1$ from the left vs. the right?
2. How does the cubic term in the numerator affect the overall behavior near $x = 1$?
3. What is a vertical asymptote, and does this function have one?
4. How do you analyze limits involving higher powers in the denominator like $(x - 1)^3$?
5. How does simplifying complex rational functions help understand their behavior?

Tip: Always check the signs of the terms in the denominator and numerator when considering limits, especially when approaching points where the denominator can be close to zero.