|
Question 128268This question is from textbook Algebra 2
: How do i identify horizontal and vertical asymptotes of functions
This question is from textbook Algebra 2
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Vertical asymptotes occur where the denominator of a rational function are zero.
There is an exception to this, however. If a rational function has the same
factor in numberator and denominator there is a hole in the finction, not
a vertical asymptote.
----------------------
Horizontal asymptote occurs in a rational function where y = p/q,
where p and q are the coefficient of the highest power term that
occurs in the numerator OR the denominator.
-------------------------------------------
Example:
f(x) = [(x-3)(x+2)]/[(x+2)(2x+5)]
-------------
Hole: at x=-2 because there is a factor of (x+2) in numerator and denominator.
-------------
Vertical Asymptote: at x = -5/2 because (2x+5) is in the denominator.
----------------
Horizontal Asymptote: at y = 1/2 because the highest power term in numerator
and denominator is x^2; you have 1x^2/2x^2 = 1/2
--------------------------
Hope this helps.
Cheers,
Stan H.
|
|
|
| |
