VA
Find the Vertical Asymptote:
(x+3)/((x-2)(x+5)
x = 2, x = -5
How do you find the horizontal asymptote when the numerator and denominator are the same degree?
y = the leading coefficients of the numerator over the denominator
The domain of a rational function consists of all real numbers except _________.
Discontinuities (Asymptotes, holes)
How do we find the y-intercept of a rational function?
Plug zero in for x
What is a rational function?
A function such that the numerator and denominator are both polynomials.
Explain the steps in finding a vertical asymptote of a rational function.
Factor/simplify, cross out any holes, set factors of denominator equal to zero, solve for x.
Find the HA:
(4x)/(x^2-1
y = 0
Write the domain of the function:
f(x)=(x+1)/((x+2)(x-7)
(-oo,-2)(-2,7)(7,oo)
How do we find the x-intercept of a rational function?
Set the numerator equal to zero and solve for x.
Name all the types of discontinuities that we have learned.
Vertical Asymptote, Horizontal Asymptote, Oblique Asymptote, Hole
Find the vertical asymptote:
(3x+4)/(4-x)
x=4
Give an example of a rational function that would have an oblique asymptote.
Anything with a numerator with exactly one higher degree than the denominator.
Find the domain:
f(x)=(x+2)/(x^2+2x-15
(-oo,-5)(-5,3)(3,oo)
Find the y intercept:
(x^2-9)/(x^2+2
(0, -9/2)
Find the y-intercept:
y=(x^3+3x+1)/(x^2-4
(0,-1/4)
Find the vertical asymptote:
(x^2-2x-3)/(x+1
No Vertical Asymptote
Find the asymptote:
(x^2-9)/(x+10
y = x-10
Find the domain:
(x^2-1)/(x^2-2x-3
(-oo,3)(3,oo)
Find the x intercept(s):
f(x)=(x^2-3x-10)/(x^2-8
(-2,0) and (5,0)
Find the asymptotes (vertical, horizontal, or slant):
VA: x=2, SA y=2x+3