Let's match the items from Column A with the appropriate items from Column B.

Here is the reasoning:

1. X-intercept: This occurs when $y = 0$, which happens when the numerator of the function equals zero. This is a point of the form $(x, 0)$.

   • So, 1 → D (X, 0).

2. Y-intercept: This occurs when $x = 0$, meaning the function is evaluated at $x = 0$, leading to a point of the form $(0, y)$.

   • So, 2 → E (0, Y).

3. Zero of the function: This also happens when $y = 0$, which again is when the numerator is zero.

   • So, 3 → A Zero of the numerator.

4. Vertical asymptote: A vertical asymptote occurs when the denominator of a rational function is zero (but the numerator is not zero).

   • So, 4 → B Zero of the denominator.

5. Horizontal asymptote: A horizontal asymptote exists when the degree $n$ of the numerator is less than the degree $d$ of the denominator, and the function approaches $y = 0$ as $x$ goes to infinity.

   • So, 5 → C Y = 0 if n < d.

Final Matching:

1. 1 → D
2. 2 → E
3. 3 → A
4. 4 → B
5. 5 → C

Would you like more details or have any questions about this matching? Here are some related questions to expand your understanding:

1. What happens to the graph of a function at a vertical asymptote?
2. How do you find the x-intercept of a rational function?
3. Can a function have more than one horizontal asymptote?
4. What does it mean for a function to have no x-intercept?
5. How do you determine the behavior of a rational function near its vertical asymptotes?

Tip: The degrees of the numerator and denominator in a rational function determine the existence and location of horizontal asymptotes.