Question

How do you find the equations of the vertical and horizontal asymptotes for a graph when you only have the graph and no function?

Answer 1

See below for answer and explanations (as well as an attached graph)

Explanation:

Pay attention to the behavior of the asymptotes. If the asymptotes are approaching a certain x-value or y-value, then that value is undefined for the function.

Take for example
`y=(1)/(x)`:

• As x approaches ∞ and -∞, then y approaches 0, which is our horizontal asymptote

• As y approaches ∞ and -∞, then x approaches 0, which is our vertical asymptote

See the graph for a visual.