John was graphing a function and noticed that at certain points, the graph reaches invisible lines the graph will never cross. Explain to John what the two types of invisible lines are and how to predict them. You may create your own example to aid in your reasoning. Use complete sentences.

Question

roadjester · Answer

The "invisible lines" are asymptotes.

anonymous · Answer

ok but what are the two types? @roadjester

anonymous · Answer

@fc3857 @Luigi0210 @PandaPrincess181 @yellowlegoguy99 @esshotwired

anonymous · Answer

vertical ones and horizontal ones i guess is what it means

anonymous · Answer

this question is confusing

anonymous · Answer

vertical ones are where the function is undefined, usually at a zero of the  denominator

anonymous · Answer

like for example $y=\frac{x}{x-1}$ would have a vertical asymptote at $x=1$

anonymous · Answer

horizontal ones are what the function approaches as $x$ goes to $\infty$ or $-\infty$
for example $y=\frac{x}{x-1}$ would have a horizontal asymptote at $y=1$

anonymous · Answer

ok but how could you predict them

anonymous · Answer

if you have a function that is one polynomial over another, a "rational function" then the vertical asymptote is where the denominator is equal to zero
for example if i had 
$$y=\frac{x+3}{x-2}$$ and set $x-2=0$ i get $x=2$ and the vertical line $x=2$ is the vertical asymptote