Question

1. find the horizontal asymptote for $y = \frac{4x^2}{2x^2 + 1}$

options:
$y = 2$
none
$y = 0$
$y = 4$

Explanation:

Step1: Identify degrees of numerator and denominator

The numerator \(4x^2\) has degree 2, denominator \(2x^2 + 1\) has degree 2.

Step2: Take ratio of leading coefficients

Leading coefficient of numerator is 4, denominator is 2. Ratio: \(\frac{4}{2} = 2\)

Step3: Determine horizontal asymptote

Since degrees are equal, asymptote is \(y = 2\)

Answer:

y = 2