Vocabulary Simplifiying Finding Asymptotes Solving Holes
Having gaps in a graph.
What is discontinuous?
x-2
What is x^2-5x+6/x-3 simplified?
y= 2
What is the horizontal asymptote for y= 2x/x-3?
x=1/4
1/x - 1 = 3/4x
(2, 4)
Where is the hole for y=x^2-4/x-2?
The graph is a smooth unbroken curve.
What is continuous?
x+4
What is x^2+2x-8/x-2 simplified?
x= 1
x= -1
What is the vertical aysmptote for y=2x/x^2-1?
x= -7
x= 4
7/x+3=x/4
(8, 11/8)
Where is the hole for y=x^2-5x-24/x^2-8x?
When the polynomial in the numerator is a higher degree then the polynomial in the denominator.
What is a slant asymptote?
x/2
What isx^2-3x/2x-6 simplified?
There is no horizontal asymptote.
What is the horizontal asymptote for y=x^2/2x-5?
x= 6
x= -4
x/x+3 = 8/x+6
(-2, 3/5)
Where is the hole for y= x^2+x-2/x^2-x-6?
Horizontal lines that the graph of a function approaches as x goes to positive and negative infinity.
What is a horizontal asymptote?
2x/3
What is 4x^2/6x simplified?
x=0
What is the vertical aysmptote for y=x^2+3x-4/x?
x=2
x=1
x/x-1 - 2/x = 1/ x-1
(-1, -1/4)
Where is the hole for y=1/x-3?
Vertical lines near which the function grows without bound.
What is a vertical asymptote?
x(x+1)
What is x^4+2x^3+x^2/x^2+x simplified?
y=9/5
What is the horizontal asymptote for y= 9x/5x-2?
x=-69
x-5/10 - x+2/5 = 6
(1.5, -2)
Where is the whole for y=2x-3/(x-2)(2x-3)?

# Rationals

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