Definitions
What is a Horizontal Asymptote?
Horizontal line that gets closer to the rational function curve as it approaches infinity
(2x-4)/x-2
Hole at x = 2
What is the domain for
2x+ 2/ x- 1
{ x ∈ ℝ, x ≄ 1}
(-∞, 1) U (1, ∞)
What is the H.A of
2x + 1 / 4x + 2
H.A is at y = 1/2
What is a Hole?
Empty area on a graph that show a function is undefined at specific points
x-4/x-5
No.
V.A at x = 5
Whats the range for
2x-1/x-1
{ y ∈ ℝ, y ≄ 2 }
(-∞, 2) U (2, ∞)
Whats the H.A of
12x+45 / 32x+64
H.A is at y = 3/8
What type of asymptote are associated with Middle Behaviors in Graphs?
Vertical Asymptotes
4x-8 / 2x-4
Hole at x = 2
Whats the domain for 3x + 4/ 4x+5
{ x ∈ ℝ, x ≄ -5/4 }
(-∞, -5/4) U (-5/4 ∞)
Whats the V.A of
7x+9 / 3x+5
V.A is at x = -5/3
What type of asymptote are associated with End Behaviors in Graphs?
Horizontal Asymptote
2x-2 /x-1
Hole at x = 1
Whats the range for
4x-8 +/ 3x + 12
{ y ∈ ℝ, y ≄ 4/3 }
(-∞, 4/3) U (4/3, ∞)
Whats the V.A of
12x+45 / 32x+64
V.A is at x = -2
What type of Rational Function is (ax+b)/(cx+d) Functions
Improper
12x-24 / x-12
No.
V.A at x = 12
Whats the Domain and Range for
12x-24/ 3x - 12
{ x ∈ ℝ, x ≄ 4 }
(-∞, 4 U (4, ∞)
{ y ∈ ℝ, y ≄ 4 }
(-∞, 4) U (4, ∞)
What is the V.A and H.A of
144x+34 / 12x+48
V.A is at x = -4
H.A is at y = 12