Asymptotes are the line(s) that the graph of a function approaches but will never touch.

Example 1
In the graph below the line approaches the x-axis, but never touches it no matter how far we extend the graph horizontally.
You may also notice that the graph approaches the y-axis, but never touches it no matter how far we extend the graph vertically.

Example #1

Example 2
In viewing the graph below, you will see that the lines approach the x-axis but never touch it. The x-axis would be a horizontal asymptote. The equation x = 0 can also be used to describe the horizontal asymptote.
The lines for the graph below also seem to approach a vertical asymptote.

Example #2

Further Discussion

What is the equation for the vertical asymptote in Example #2?

How can we determine if an equation has a vertical or horizontal asymptote without graphing

EF-100 (The only asymtote problem I could find from this year)
Sophia Moreno

Graph

Name intercepts, domain and range

The asymptote is y = -1
The line will approach Y = -1, but never reach it.

Asymptotes are the line(s) that the graph of a function approaches but will never touch.What are Asymptotes?Example 1In the graph below the line approaches the x-axis, but never touches it no matter how far we extend the graph horizontally.

You may also notice that the graph approaches the y-axis, but never touches it no matter how far we extend the graph vertically.

Example 2In viewing the graph below, you will see that the lines approach the x-axis but never touch it. The x-axis would be a horizontal asymptote. The equation x = 0 can also be used to describe the horizontal asymptote.

The lines for the graph below also seem to approach a vertical asymptote.

Further DiscussionEF-100(The only asymtote problem I could find from this year)Sophia Moreno

Graph

Name intercepts, domain and range

The asymptote is y = -1

The line will approach Y = -1, but never reach it.