Unit 1 B

Question 1

what is a rational function?

Answer 1

a ratio of polynomials that could have horizontal vertical, or slant asymptotes

Question 2

end behavior for a rational function always refers to…

Answer 2

horizontal asymptotes

Question 3

if numerator’s degree is less than denominator’s degree

Answer 3

the HA is at y=0
as x > +/- inf f(x)=0

Question 4

if numerator’s degree is equal to denominator’s degree

Answer 4

the HA is at leading co of num/leading co of de
as x > +/- inf f(x)=a/b

Question 5

if numerator’s degree is more than denominator’s degree

Answer 5

no HA
as x > +/- inf f(x)=+/- inf

Question 6

if the degree of the numerator is exactly one more than the degree of the denominator…

Answer 6

f(x) has a slant (oblique) asymptote

Question 7

slant asymptotes…

Answer 7

are parallel to y=a/bx (same slope)

Question 8

a rational function will have zeros where…

Answer 8

the numerator is zero

Question 9

a rational function will have vertical asymptotes where…

Answer 9

the denominator is zero

Question 10

the f(x) and g(x) share a factor that will be…

Answer 10

a whole in the graph

Question 11

to solve rational inequalities…

Answer 11

find zeros and VAs, use sign chart, test points

Question 12

to subtract fractions you must…

Answer 12

first find a LCD

Question 13

vertical asymptotes are…

Answer 13

factors in the denominator that don’t cancel

Question 14

limits when there is a whole

Answer 14

equal hole

Question 15

limits with VA

Answer 15

+/- inf

Question 16

when writing an equation…

Answer 16

find holes and vas, make sure wholes add up, make sure multiplicity is correct for VAs (if same sign for limits should be even)

Question 17

when squaring an exponent

Answer 17

square the coefficient too

Question 18

when making sign charts always include

Answer 18

holes

Question 19

binomial theorem

Answer 19

(a+b)^n= (n choose zero up to n choose n) (a to the n to a to the zero) (b to the zero to b to the n)

Question 20

paschal’s triangle

Answer 20

row one is for zero, start with one and add down

Question 21

domain of a rational function

Answer 21

everything except holes and VAs

Question 22

to find a slant asymptote..

Answer 22

perform division (can disregard remainder)

Question 23

vertical shift

Answer 23

f(x)+k

Question 24

horizontal shift

Answer 24

f(x+k)

Question 25

horizontal transformations act…

Answer 25

opposite to how you would think they would

Question 26

vertical dilation

Answer 26

a*f(x) (take abs. value of a)
if a is negative will be a reflection over the x axis

Question 27

horizontal dilation

Answer 27

f(ax) (by a factor of 1/b)
if b is negative it will be a reflection over the y axis

Question 28

linear

Answer 28

constat roc

Question 29

quadratic

Answer 29

2nd diff constant

Question 30

inverse variation

Answer 30

y=k/x
k is a constant of proportionality