Definitions
A function that has a polynomial both in the Numerator and in the Denominator
What is a Rational Function?
When the Multiplicity on the top of a rational function is bigger than the one on the bottom or equal
What is a Hole?
g(x)=-x4+2x3+5x2-1
As X -> infinity, g(x) -> -infinity and As X -> -infinity, g(x) -> -infinity
What are the horizontal asymptotes of the following function
x/(x-27)(x+25)
x = 27 and x = -25
f (x) = x + 1 /x - 2
Vertical Asymptotes : x = 2
Holes: None
Horizontal Asymptotes: y = 1
X-intercepts: -1
The number that multiplies the number with the highest degree
What is a Leading Coefficient?
When the multiplicity of the bottom is larger than the one on the bottom
What is a Vertical Asymptote?
f(x) = 3x3 + 10x2 + 4x -8
As X -> infinity, g(x) -> infinity and As X -> -infinity, g(x) -> -infinity
What are the horizontal asymptotes of the following function
(2x+24)(28-x)/(3x+18)(x-5)
x = -6 and x = 5
f (x) = x 3+ x 2 - 12x/ x 3 - x 2 - 6 x
Vertical Asymptotes : x = -2
Holes: x = 0, x = 3
Horizontal Asymptotes: y = 1
X-intercepts: -4
The number of times a Zero of a Function appears.
What is Multiplicity?
When the a zero only appears on the top
What is a X-intercept?
q(x)=3x4-5x3-2x2+x-18
As X -> infinity, g(x) -> infinity and As X -> -infinity, g(x) -> infinity
What are the Vertical asymptotes of the following function
7x2+ 14x + 28/3x2 + 12x + 9
y = 7/3
f(x) = = 3x2 - 3x - 18/x2 - 4
Vertical Asymptotes : x = 2
Holes: x = -2
Horizontal Asymptotes: y = 3
X-intercepts: 3
A asymptote that only occurs when the Degree on the top of a Rational function is exactly 1 higher than the Degree on the Bottom
What is a Slant Asymptote?
When a Zero Only appears on the bottom
What is a Vertical Asymptote?
q(x)=-2x^8+5x^6-3x^5+50
As X -> infinity, g(x) -> -infinity and As X -> -infinity, g(x) -> -infinity
What are the holes of the following function
(x-34)(x-3)/(x-2)(x-3)
x=-3
What is the end behavior of -x7 - 5x +2
As X -> infinity, g(x) -> -infinity and As X -> -infinity, g(x) -> infinity
The way a function acts when a very big or very small number is inputed into a function.
What is End Behavior?
When a functions degree is even and the leading coefficient is negative the end behavior will always go towards
What is Negative Infinity
g(x)=10x9-50x6-500x2
As X -> infinity, g(x) -> infinity and As X -> -infinity, g(x) -> -infinity
What are the slant asymptotes of the following function
3x3 -1/x2 + 2x
Slant Azymptote = 3x-6
Remainder = 12x - 1
What is the end behavior of x46 + 3x - 1
As X -> infinity, g(x) -> infinity and As X -> -infinity, g(x) -> infinity