Find the horizontal asymptote of the graph of each rational function.
Problem 1 :
y = 2/(x – 6)
Problem 2 :
y = (x + 2)/(x – 4)
Problem 3 :
y = (x + 3)/2(x + 4)
Problem 4 :
y = (2x2 + 3)/(x2 – 6)
Problem 5 :
y = (3x - 12)/(x2 – 2)
Problem 6 :
y = (3x3 – 4x + 2)/(2x3 + 3)
1) y = 0
2) y = 1
3) y = 1/2
4) y = 2
5) y = 0 which is the x – axis.
6) y = 1.5.
Find the oblique asymptote of the rational functions.
Problem 1 :
f(x) = (x2 + 8x – 20)/(x – 1)
Problem 2 :
f(x) = (6x3 – 1)/(-2x2 + 18)
Problem 3 :
f(x) = (2x2 + x – 5)/(x + 1)
Problem 4 :
f(x) = (2x2 - 5x + 3)/(x – 1)
Problem 5 :
f(x) = (2x2 - 5x + 5)/(x – 2)
Problem 6 :
f(x) = (x3 - 2x2 + 5)/x2
Problem 7 :
f(x) = (x3 - x2 - x - 1)/(x – 3) (x + 4)
Problem 8 :
f(x) = x3/(x2 – 4)
1) y = x + 9
2) y = -3x
3) y = 2x - 1
4) y = 2x + 3
5) y = 2x + 1
6) y = x + 2
7) y = x – 2
8) Vertical asymptotes at x = -2 and 2
Oblique asymptote is at y = x-4
x-intercept is at x = 0
y-intercept is at x = 0
Describe the vertical asymptotes and holes for the graph of each rational function.
Problem 1 :
y = (x - 2)/(x + 2) (x - 2)
Problem 2 :
y = x/x(x - 1)
Problem 3 :
y = (5 - x)/(x2 - 1)
Problem 4 :
y = (x2 - 2)/(x + 2)
Problem 5 :
y = (x2 - 4)/(x2 + 4)
Problem 6 :
y = (x + 3)/(x2 - 9)
Problem 7 :
y = (x2 - 25)/(x – 4)
Problem 8 :
y = (x - 2) (2x + 3)/(5x + 4) (x – 3)
Problem 9 :
y = (15x2 - 7x - 2)/(x2 - 4)
1) Vertical asymptote at x = -2; hole at x = 2
2) Vertical asymptote at x = 1; hole at x = 0
3) Vertical asymptotes at x = 1 and x = -1
4) Vertical asymptote at x = -2
5) No vertical asymptotes and no holes
6) Vertical asymptote at x = 3; hole at x = -3
7) Vertical asymptote at x = 4
8) Vertical asymptotes at x = -4/5 and x = 3.
9) Vertical asymptotes at x = 2 and x = -2.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM