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AP PreCalculus > Unit 2: Polynomial and Rational Functions > Flashcards

Unit 2: Polynomial and Rational Functions Flashcards

1
Q

n is the (blank) of the polynomial

A

degree

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2
Q
A

leading coefficient

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3
Q

Relative maximum is when…

A

a function changes from increasing to decreasing

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4
Q

Relative minimum is when…

A

a function changes from decreasing to increasing

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5
Q

Absolute maximum is…

A

the highest y-value of the function at some x

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6
Q

Absolute minimum is…

A

the lowest y-value of the function at some x

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7
Q

The degree of the polynomial is equal to…

A

the constant nth difference

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8
Q

relative extrema are also called…

A

local extrema

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9
Q

absolute extrema are also called…

A

global extrema

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10
Q

Inflection point

A

where function changes concavity

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11
Q

multiplicity is…

A

the number of times a factor occurs

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12
Q

If multiplicity is one…

A
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13
Q

If multiplicity is three…

A
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14
Q

If multiplicity is even…

A
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15
Q

How many zeros can a polynomial have?

A

The same as the degree including multiplicity

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16
Q

quadratic formula

A
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17
Q

complex zeros come in…

A

conjugate pairs

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18
Q

Even function is symmetric…

A

over the y-axis

19
Q

Odd function is symmetric…

A

about the origin

20
Q

For an even function plugging in opposite x-values will give you…

A

same y-values

21
Q

For an odd function plugging in opposite x-values will give you…

A

opposite y-values

22
Q

What type of end behavior is this?

A

Left end behavior

23
Q

What type of end behavior is this?

A

Right end behavior

24
Q

Describe left end behavior verbally

A

“As the x values decrease without bound, the y values of f(x)…”

25
Q

Describe right end behavior verbally

A

“As the x values increase without bound, the y values of f(x)…”

26
Q

If function has a positive leading coefficient then…

A

the right end goes to infinity

27
Q

If function has a negative leading coefficient then…

A

the right end goes to negative infinity

28
Q

If the degree of the polynomial is even then…

A

the left end goes in the same direction as the right end

29
Q

If the degree of the polynomial is odd then…

A

the left end goes in the opposite direction as the right end

30
Q

(x , y) -> ( -x , y ) is what type of function?

A

even because opposite x values give same y values

31
Q

(x , y) -> (-x , -y) is what type of function?

A

opposite because opposite x values give opposite y values

32
Q

Rational functions are…

A

a ratio of two polynomials

33
Q

When does a rational function have a horizontal asymptote at y=a/b?

A

When the leading terms in the numerator and denominator have the same degree

n=d

34
Q

When does a rational function have a horizontal asymptote at y=0?

A

When the degree of the numerator is less than the degree of the denominator

n<d

35
Q

When does a rational function have a slant asymptote?

A

When degree of the numerator is exactly 1 more than the degree of the denomiator

n=d+1

36
Q

When does a rational function have no horizontal asymptote?

A

When the degree in the numerator is greater than the degree in the denominator

n>d

37
Q

graphs of rational functions can never cross…

A

vertical asymptotes

38
Q

A rational function has an x-intercept when…

A

the number where ONLY the factor in the numerator is zero

39
Q

a rational function has a hole when…

A

same factor is in numerator and denominator

40
Q

a rational function has a vertical asymptote when…

A

the number where ONLY the factor in the denominator is zero

41
Q

rational functions can represent…

A

division problems

42
Q

Here shows the division of a rational function. Name each part of the division.

A
43
Q

How do you know if a rational function has a slant asymptote?

A

A slant asymptote occurs if the quotient function is a linear function.

44
Q

Build Pascal’s Triangle for a binomial expansion to the 7th power.

A

AP PreCalculus (5 decks)

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