SOLUTION: what are the x and y intercepts and horizontal and vertical asymtotes for the equation y=4-x/5x^2-4x-1 and how do you graph it

Algebra ->  Rational-functions -> SOLUTION: what are the x and y intercepts and horizontal and vertical asymtotes for the equation y=4-x/5x^2-4x-1 and how do you graph it       Log On


   

Question 21017: what are the x and y intercepts and horizontal and vertical asymtotes for the equation
y=4-x/5x^2-4x-1
and how do you graph it
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
y=%284-x%29%2F%285x%5E2-4x-1%29

Factor the denominator:
y=%284-x%29%2F%28%285x%2B1%29%28x-1%29%29
X-intercept is where y = 0. The only way a fraction can equal zero is if the numerator equals zero, which occurs at x= 4.

Y-intercept is where x= 0. y=+4%2F-1=+-4

Horizontal asymptote: Degree of the numerator is less than the degree of the denominator, so y=0 (the x-axis) is the horizontal asymptote.

Vertical asymptotes: Values that would make the denominator factors equal zero. This would be at x= -1/5 and x= 1.
graph%28600%2C600%2C-4%2C6%2C-8%2C4%2C%284-x%29%2F%285x%5E2-4x-1%29%29

R^2 at SCC