Question

could someone give me assistance with this question/

Answer 1

The asymptote of the function f(x) = 3x + 4 is y =

Answer 2

Well, an asymptote is a line it does not cross. Is there any line that does not cross?

Answer 3

Well... vertical ones it does not cross. Here is a better definition:
https://www.mathsisfun.com/algebra/asymptote.html

Answer 4

I guess you have to find horizontal asy.

for \(\color{green}{\rm Vertical~ asy.}\)
set the denominator equal to zero and then solve for the variable.
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

Answer 5

Slant asy when the highest degree of the denominator is one less than the highest degree of the numerator.

don't know about oblique i guess slant and oblique both are the same hmmm? not sure

Answer 6

Yes, oblique and slant are the same. But what he gave was a line... so not sure what would apply.

Answer 7

ohh cool. thanks