|
Question 151671This question is from textbook
: Can someone please help I don't understand. Find the equations for the horizontal and vertical asymptotes of the following.
A. f(x)=2x+1/x-4
B. g(x)=3x/x^2-4
What is the horizontal vertical for both equations? Thank you
This question is from textbook
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! A)
 Start with the given function
Looking at the numerator  , we can see that the degree is  since the highest exponent of the numerator is . For the denominator  , we can see that the degree is since the highest exponent of the denominator is .
Horizontal Asymptote:
Since the degree of the numerator and the denominator are the same, we can find the horizontal asymptote using this procedure:
To find the horizontal asymptote, first we need to find the leading coefficients of the numerator and the denominator.
Looking at the numerator , the leading coefficient is 
Looking at the denominator , the leading coefficient is
So the horizontal asymptote is the ratio of the leading coefficients. In other words, simply divide by to get 
So the horizontal asymptote is 
--------------------------------------------------
Vertical Asymptote:
To find the vertical asymptote, just set the denominator equal to zero and solve for x
 Set the denominator equal to zero
 Add 4 to both sides
 Combine like terms on the right side
So the vertical asymptote is
Notice if we graph  , we can visually verify our answers:
 Graph of with the horizontal asymptote (blue line) and the vertical asymptote (green line)
B)
 Start with the given function
Looking at the numerator  , we can see that the degree is since the highest exponent of the numerator is . For the denominator  , we can see that the degree is since the highest exponent of the denominator is .
Horizontal Asymptote:
Since the degree of the numerator (which is ) is less than the degree of the denominator (which is ), the horizontal asymptote is always 
So the horizontal asymptote is
--------------------------------------------------
Vertical Asymptote:
To find the vertical asymptote, just set the denominator equal to zero and solve for x
 Set the denominator equal to zero
 Add 4 to both sides
 Combine like terms on the right side
 or  Take the square root of both sides
Notice if we graph  , we can visually verify our answers:
 Graph of with the horizontal asymptote (blue line) and the vertical asymptotes and (green lines)
|
|
|
| |
