Part 3/6:
where ( L ) is a finite constant. Essentially, if a function approaches a certain horizontal line as ( x ) elongates to infinity, that line represents a horizontal asymptote.
Graphically, one can imagine a function whose output stabilizes at a specific height (L) as you continue to move right or left along the x-axis.
Analyzing Asymptotes Through Examples
Example 1: The Function ( y = \frac{1}{x} )
To identify the asymptotes of ( y = \frac{1}{x} ):
For the vertical asymptote, plugging in ( x=0 ) yields division by zero, indicating a vertical line ( x = 0 ).
As ( x ) approaches positive infinity, ( y ) approaches 0, leading to a horizontal asymptote at ( y = 0 ).