math 2: rational functions Flashcards

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1
Q

rational function:

A

f(x) = p(x)/ q(x)

p(x) and q(x) are polynomial functions and q(x) ≠ 0

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2
Q

as a general rule, graphs of rational functions are not

A

continuous

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3
Q

a point of discontinutiy occurs at any value of

A

x where q(x) = 0

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4
Q

if p(x) & q(x) can be factored so that f(x) can be reduced, removing the factors that caused the discontinuities, the graph will contain only

A

holes

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5
Q

if the factors that caused the discontinuities cannot be removed,

A

asymptotes will occur

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6
Q

asymptotes can be described using

A

limit notation

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7
Q

limx→∞ f(x)=0 means f(x) gets closer to 0 as

A

x gets large/ small

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8
Q

limx→2+ = ∞ means f(x) gets arbitrarily large as x approaches

A

2 from the right

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