To determine the horizontal asymptote of the function:

$y = \frac{4x + 4}{2x^2 + 12x - 12}$

we need to analyze the degrees of the polynomial in the numerator and the denominator.

1. Degree of the numerator: The highest degree term in the numerator is $4x$, which has degree 1.
2. Degree of the denominator: The highest degree term in the denominator is $2x^2$, which has degree 2.

When the degree of the denominator is greater than the degree of the numerator, the horizontal asymptote is $y = 0$.

Thus, the correct answer is:

d) $y = 0$.

Additional Details:

• When the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is always $y = 0$.
• If the degrees were the same, you would divide the leading coefficients to find the horizontal asymptote.

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Would you like further clarification or any other questions related to horizontal asymptotes?

Here are some related questions:

1. What happens to the horizontal asymptote if the degrees of the numerator and denominator are the same?
2. How do you find the vertical asymptotes of a rational function?
3. What is the behavior of a rational function at infinity?
4. How do you graph a rational function based on its asymptotes?
5. How does the horizontal asymptote relate to limits at infinity?

Tip: Always compare the degrees of the numerator and denominator first to determine if there is a horizontal asymptote.