Graphing rational functions

[FMMurphy]

I have a problem which is: y = 2x + 3/ x +4 I am to find the horizontal and vertical asymptotes of the graph of the function. I know how to get the
vertical x = -4 and I know the horizontal answer is 2 but I don't know how they got the y = 2? Could you please explain the procedure of finding the horizontal? Thanks

 

[galactus]

If the power of the numerator is equal to the power of the denominator, then

the line \(\displaystyle y=\frac{a_{n}}{b_{k}}\)(the ratio of leading coefficients) is the asymptote.

You have \(\displaystyle \frac{2x+3}{x+4}\)

\(\displaystyle \frac{a_{n}}{b_{k}}=\frac{2}{1}=2\)

See?.

 

[tkhunny]

vertical x = -4

I know the horizontal answer is 2 but I don't know how they got the y = 2?

Why would one asymptote be an equation of a line and the other asymptote just a number?

A vertical asymptote is a vertical line. It has an equation like this: x = a
A horizontal asymptote is a horizontal line. It has an equation like this: y = a

 

[jwpaine]

I created this for my pre-calculus peers,

http://jpaine.net/math/rational.pdf

Hope this helps!