Unit 2: Polynomial and Rational Functions

Question 1

n is the (blank) of the polynomial

Answer 1

degree

Question 2

Answer 2

leading coefficient

Question 3

Relative maximum is when…

Answer 3

a function changes from increasing to decreasing

Question 4

Relative minimum is when…

Answer 4

a function changes from decreasing to increasing

Question 5

Absolute maximum is…

Answer 5

the highest y-value of the function at some x

Question 6

Absolute minimum is…

Answer 6

the lowest y-value of the function at some x

Question 7

The degree of the polynomial is equal to…

Answer 7

the constant nth difference

Question 8

relative extrema are also called…

Answer 8

local extrema

Question 9

absolute extrema are also called…

Answer 9

global extrema

Question 10

Inflection point

Answer 10

where function changes concavity

Question 11

multiplicity is…

Answer 11

the number of times a factor occurs

Question 12

If multiplicity is one…

Answer 12

Question 13

If multiplicity is three…

Answer 13

Question 14

If multiplicity is even…

Answer 14

Question 15

How many zeros can a polynomial have?

Answer 15

The same as the degree including multiplicity

Question 16

quadratic formula

Answer 16

Question 17

complex zeros come in…

Answer 17

conjugate pairs

Question 18

Even function is symmetric…

Answer 18

over the y-axis

Question 19

Odd function is symmetric…

Answer 19

about the origin

Question 20

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

Answer 20

same y-values

Question 21

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

Answer 21

opposite y-values

Question 22

What type of end behavior is this?

Answer 22

Left end behavior

Question 23

What type of end behavior is this?

Answer 23

Right end behavior

Question 24

Describe left end behavior verbally

Answer 24

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

Question 25

Describe right end behavior verbally

Answer 25

"As the x values increase without bound, the y values of f(x)..."

Question 26

If function has a positive leading coefficient then...

Answer 26

the right end goes to infinity

Question 27

If function has a negative leading coefficient then...

Answer 27

the right end goes to negative infinity

Question 28

If the degree of the polynomial is even then...

Answer 28

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

Question 29

If the degree of the polynomial is odd then...

Answer 29

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

Question 30

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

Answer 30

even because opposite x values give same y values

Question 31

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

Answer 31

opposite because opposite x values give opposite y values

Question 32

Rational functions are...

Answer 32

a ratio of two polynomials

Question 33

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

Answer 33

When the leading terms in the numerator and denominator have the same degree | n=d

Question 34

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

Answer 34

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

Question 35

When does a rational function have a slant asymptote?

Answer 35

When degree of the numerator is exactly 1 more than the degree of the denomiator | n=d+1

Question 36

When does a rational function have no horizontal asymptote?

Answer 36

When the degree in the numerator is greater than the degree in the denominator | n>d

Question 37

graphs of rational functions can never cross...

Answer 37

vertical asymptotes

Question 38

A rational function has an x-intercept when...

Answer 38

the number where ONLY the factor in the numerator is zero

Question 39

a rational function has a hole when...

Answer 39

same factor is in numerator and denominator

Question 40

a rational function has a vertical asymptote when...

Answer 40

the number where ONLY the factor in the denominator is zero

Question 41

rational functions can represent...

Answer 41

division problems

Question 42

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

Answer 42

Question 43

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

Answer 43

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

Question 44

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

Answer 44