# How do you find the vertical, horizontal or slant asymptotes for #f(x)= (4x+8)/(x-3)#?

##### 2 Answers

#### Explanation:

Take the denominator set it equal to 0 and solve for x to find the vertical asymptote. To find the horizontal asymptote find the limit as x goes to infinity and use the end behavior of a rational function. That is, pick the highest degree term from the top and bottom then simplify

Slant Asymptote: None

#### Explanation:

At

Similarly, no matter how far the graph of the function increases or decreases to the right or to the left respectively, the line approached by the graph is

Therefore

See the graph of

graph{(y- (4x+8)/(x-3))=0[-40,40,-20,20]}

See also the graph of the asymptotes

graph{(y-4)(y+(1000)x-3*(1000))=0[-40,40,-20,20]}

God bless ... I hope the explanation is useful