Question

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.

Answer 1

The "invisible lines" are asymptotes.

Answer 2

ok but what are the two types? @roadjester

Answer 3

@fc3857 @Luigi0210 @PandaPrincess181 @yellowlegoguy99 @esshotwired

Answer 4

vertical ones and horizontal ones i guess is what it means

Answer 5

this question is confusing

Answer 6

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

Answer 7

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

Answer 8

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 \(y=1\)

Answer 9

ok but how could you predict them

Answer 10

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