If \(y=\frac{12x^4+4x^3+9x^2+5x+3}{3x^4+2x^3+8x^2+3x+1}\), at what value of y will there be a horizontal asymptote?
This is a "same degree / same degree" rational function
The horizontal asymptote will be y = the ratio of the coefficients on both of the 4th power terms in the numerator/ denominator
So the horizontal asymptote is
y = 12 / 3 = 4
Se the graph here to confirm this :
https://www.desmos.com/calculator/hjmx53zp3d