Question

ponential, and logarithmic for which a function is increasing or horizontal asymptotes. Iy sim y²-3y/4y+12-(12-2y)/(4y+12)

Answer 1

To determine if a function is increasing or has horizontal asymptotes, we need to analyze its behavior as x approaches positive or negative infinity. The given function does not have any horizontal asymptotes.

Step-by-step explanation:

To determine if a function is increasing or has horizontal asymptotes, we need to analyze its behavior as x approaches positive or negative infinity. Let's analyze the given function:

f(x) = (y^2 - 3y) / (4y + 12) (12 - 2y) / (4y + 12)

1. Let's simplify the function by combining like terms:
2. f(x) = (y(y-3)) / (4y + 12) (12 - 2y) / (4y + 12)
3. Now, let's find the limits as x approaches infinity and negative infinity:
4. As x approaches infinity, both the numerator and denominator of the function tend to infinity, so we can see that there is no horizontal asymptote in this case.
5. As x approaches negative infinity, both the numerator and denominator of the function tend to infinity, so again, there is no horizontal asymptote.

Therefore, the given function does not have any horizontal asymptotes.