## anonymous one year ago .

1. Nnesha

for$$\color{green}{\rm Horizontal ~asy.}$$ focus on highest degrees ~if the highest degree of the numerator is greater than the denominator then No horizontal asy. $\color{reD}{\rm N}>\color{blue}{\rm D}$ example $\large\rm \frac{ 7x^\color{ReD}{3} +1}{ 4x^\color{blue}{2}+3 }$ ~if the highest degree of the denominator is greater than the highest degree of the numerator then y=0 would be horizontal asy. $\rm \color{reD}{N}<\color{blue}{\rm D}$ example:$\large\rm \frac{ 7x^\color{red}{2}+1 }{ 4x^\color{blue}{3}+3 }$ ~if both degrees are the same then divide the leading coefficient of the numerator by the leading coefficient of the denominator $\rm \color{red}{N}=\color{blue}{D}$ $\large\rm \frac{ 8x^\color{reD}{3}+1 }{ 4x^\color{blue}{3}+3 }$ $\rm \frac{ 8x^3 }{ 4x^3 } =2$ horizontal asy. =2

2. Nnesha

looks long but just read two lines :D

3. Nnesha

Slant or oblique asy. if the highest degree of the denominator one lessthan the numerator then you can find slant asy. use the synthetic division y= quotient (slant asy.)