someone please help

Question

 

 

I have to sketch a graph for the rational equation with all asymptotes included where are the asymptotes and what points work for drawing the graph

 

F(x)=X^2-4/x^2-3x+2

 

Answer 1

Vertical Asymptotes

Set the denominator equal to zero.

 

x²-3x+2 = 0

(x-2)(x-1) = 0

 

x = 1 , x = 2

 

Vertical asymptote is x=1 and x=2

 

 

Horizontal Asymptotes

 

We focus on the coefficients of the term with the highest degree.  In this function, the term with the highest degree in the numerator is x² and the term with the highest degree in the denominator is x².  Since the degree of the numerator and denominator are the same, we divide their coefficients.  These are noted in bold.

 

(x²-4)/(x²-3x+2)

 

Therefore, the horizontal asymptote is 1.

 

Graph this function to check.