Question

State the horizontal asymptote of the rational function. f(x)=x^2+9x-9/x-9

Answer 1

please help im so lost

Answer 2

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.` \[\color{reD}{\rm N}>\color{blue}{\rm D}\]
~if the highest degree of the denominator is greater than the highest degree of the numerator then `y=0` would be horizontal asy.
\[\rm \color{reD}{N}<\color{blue}{\rm D}\]
~if both degrees are the same then divide the leading coefficient of the numerator by the leading coefficient of the denominator
\[\rm \color{red}{N}=\color{blue}{D}\]

Answer 3

\[\color{reD}{\rm N}>\color{blue}{\rm D}\]example\[\large\rm \frac{ 7x^\color{ReD}{3} +1}{ 4x^\color{blue}{2}+3 }\]\[\rm \color{reD}{N}<\color{blue}{\rm D}\]example:\[\large\rm \frac{ 7x^\color{red}{2}+1 }{ 4x^\color{blue}{3}+3 }\]\[\rm \color{red}{N}=\color{blue}{D}\]\[\large\rm \frac{ 8x^\color{reD}{3}+1 }{ 4x^\color{blue}{3}+3 }\] \[\rm \frac{ 8x^3 }{ 4x^3 } =2\] horizontal asy. =2
examples