SOLUTION: find the equatons of both the vertical and horizontal asymptotest of the function g(x)=5x^2-4/x+1

Click here to see ALL problems on Linear Algebra

Question 437705: find the equatons of both the vertical and horizontal asymptotest of the function g(x)=5x^2-4/x+1
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
find the equations of both the vertical and horizontal asymptote of the function g(x)=5x^2-4/x+1
..
This function has no horizontal asymptote because the degree of the numerator is greater than the degree of the denominator. Instead, it has a slant asymptote.
To find the equation of the slant asymptote, divide denominator,(x+1) into numerator(5x^2-4), by long division. You should get a quotient of (5x-5) plus a remainder of 1. (5x-5) is the equation of the slant asymptote. This is a straight line with a slope of 5 and a y-intercept of -5. To find the vertical asymptote, set the denominator=0, then solve for x.
x+1=0
x=-1
ans:
Equation of slant asymptote: 5x-5
Equation of vertical asymptote:x=-1
See the graph below: The green line is the equation of the slant asymptote. The vertical asymptote cannot be shown on the graph, but you can see it is close to x=-1.

..