ch3: rationals

Question 1

horizontal asymptote

Answer 1

• ratio of leading coefficients (# attached to highest variable)
• if not, use 0
• y =

Question 2

vertical asymptote

Answer 2

• set denominator to 0 and solve for x
• denom = bottom
• x =

Question 3

exception for vertical asymptote

Answer 3

• if top and bottom both have same factor, it cancels out nd becomes hole

Question 4

x-intercept

Answer 4

• set numerator (top) to zero and find x
• (x, 0)
• write “none” if top has no x

Question 5

y-intercept

Answer 5

• ratio of constant terms (alone number
• (0, y)

Question 6

pimple graph

Answer 6

• denom: (x^2 + #)
• no vertical asymptotes

Question 7

both sides towards vert. asymptote

Answer 7

• denom: (x -+ #)^2
• one vertical asympote

Question 8

“parabola” graph

Answer 8

• denom: (x + #)(x + #)
• two vertical asymptotes
• max/min and y-int

Question 9

wht is a restriction

Answer 9

value of x that doesnt exist

Question 10

whts a restriction graphically

Answer 10

asymptotes or holes

Question 11

where are restrictions found in a function nd wht do they help w

Answer 11

• asymptotes found in denom, so “restrictions help create factors in denom”

Question 12

domain

Answer 12

• possible values of x
• if greater, thn graph must be above x=0 on domain

Question 13

asymptote definition

Answer 13

line that a curve approaches but never reaches as it heads towards infinity

Question 14

why do holes exist

Answer 14

same factor at top and bottom

Question 15

another word for “holes” on graph

Answer 15

discontinuity

Question 16

how do u graph regular rational functions/reciprocals of linear

Answer 16

1. find VA, HA, x-int, and y-int
2. plot all from step 1
3. make behaviour chart nd graph
4. label graph w f(x)

Question 17

what happens to domain and range when u have a hole

Answer 17

the x and y-vals add another restriction

Question 18

reciprocal of a graph w/o x-intercepts has…

Answer 18

no vertical asymptotes (pimple graph)

Question 19

reciprocal of a graph w one x-intercept has…

Answer 19

one vertical asymptotes

Question 20

reciprocal of a graph w two x-intercepts has…

Answer 20

two vertical asymptotes

Question 21

how to graph reciprocal of quadratic w/ two x-intercepts

Answer 21

1. do VA, HA, x-int, and y-into **find y-int by plugging by doing f(0) and HA is y=0
2. do behaviour chart for both vertical asymptotes
3. max/min pt: avg of both VA, then plug that val into eqn
4. domain and range (range is greater than HA and greater than/equal to max/min)

Question 22

how to graph reciprocal of quadratic w/ no x-intercepts

Answer 22

1. do VA, HA, x-int, y-int (will not have a VA)
2. behaviour chart w/ just +-infinity
3. domain is XER, range is greater than HA, less than or equal to max (y-int)

Question 23

how to graph reciprocal of quadratic w/ one x-intercepts

Answer 23

1. do VA, HA, x-int, and y-into **find y-int by plugging by doing f(0) and HA is y=0
2. do behaviour chart for both vertical asymptotes
3. max/min pt: avg of both VA, then plug that val into eqn
4. domain and range (range is …)

Question 24

solving eqns: fraction = fraction

Answer 24

cross multiply

Question 25

solving eqns: fraction +- fraction = number

Answer 25

1. common denom for fractions 2. expand and simplify: move all to one side 3. common factor

Question 26

what should u NOT do when solving rational inequalities?

Answer 26

dont cross multiply