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

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) (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:

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:

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

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