SOLUTION: Graph the rational function f(×)= -4X^2+1/X^2+X-6 A)Find the vertical asymptote(s),If they exists B)Find the horizontal asymptote, if it exists.Dont forget to check for oblique

Algebra ->  Rational-functions -> SOLUTION: Graph the rational function f(×)= -4X^2+1/X^2+X-6 A)Find the vertical asymptote(s),If they exists B)Find the horizontal asymptote, if it exists.Dont forget to check for oblique       Log On


   

Question 1136718: Graph the rational function f(×)= -4X^2+1/X^2+X-6
A)Find the vertical asymptote(s),If they exists
B)Find the horizontal asymptote, if it exists.Dont forget to check for oblique asymptote.
C)Find the x-intercept of the function.
D)Find the y-intercept of the function.
E)sketch the rational function and plot a few points if needed.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Again you should know parentheses are required....

The function is



(1) y-intercept: when x=0: -1/6

(2) x-intercept(s): where y=0; i.e., where the numerator is 0: at x=-1/2 and x=1/2

(3) vertical asymptote(s): where the denominator is 0 -- at x=-3 and x=2

(4) horizontal asymptote: y=-4 (degree of numerator and denominator are the same, so ratio of leading coefficients)

A graph of the rational function and the horizontal asymptote:

graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C%28-4x%5E2%2B1%29%2F%28x%5E2%2Bx-6%29%2C-4%29

The graph points out another thing you should look for when graphing a rational function: Does the graph cross the horizontal asymptote?

To find out, set the function equal to -4 and solve:

%28-4x%5E2%2B1%29%2F%28x%5E2%2Bx-6%29=-4
-4x%5E2%2B1+=+-4x%5E2-4x%2B24
4x+=+23
x+=+23%2F4

The graph shows the graph of the rational function crossing the asymptote y=-4 at x= 23/4 = 5.75.