ch3: rationals Flashcards
horizontal asymptote
- ratio of leading coefficients (# attached to highest variable)
- if not, use 0
- y =
vertical asymptote
- set denominator to 0 and solve for x
- denom = bottom
- x =
exception for vertical asymptote
- if top and bottom both have same factor, it cancels out nd becomes hole
x-intercept
- set numerator (top) to zero and find x
- (x, 0)
- write “none” if top has no x
y-intercept
- ratio of constant terms (alone number
- (0, y)
pimple graph
- denom: (x^2 + #)
- no vertical asymptotes
both sides towards vert. asymptote
- denom: (x -+ #)^2
- one vertical asympote
“parabola” graph
- denom: (x + #)(x + #)
- two vertical asymptotes
- max/min and y-int
wht is a restriction
value of x that doesnt exist
whts a restriction graphically
asymptotes or holes
where are restrictions found in a function nd wht do they help w
- asymptotes found in denom, so “restrictions help create factors in denom”
domain
- possible values of x
- if greater, thn graph must be above x=0 on domain
asymptote definition
line that a curve approaches but never reaches as it heads towards infinity
why do holes exist
same factor at top and bottom
another word for “holes” on graph
discontinuity
how do u graph regular rational functions/reciprocals of linear
- find VA, HA, x-int, and y-int
- plot all from step 1
- make behaviour chart nd graph
- label graph w f(x)
what happens to domain and range when u have a hole
the x and y-vals add another restriction
reciprocal of a graph w/o x-intercepts has…
no vertical asymptotes (pimple graph)
reciprocal of a graph w one x-intercept has…
one vertical asymptotes
reciprocal of a graph w two x-intercepts has…
two vertical asymptotes
how to graph reciprocal of quadratic w/ two x-intercepts
- do VA, HA, x-int, and y-into **find y-int by plugging by doing f(0) and HA is y=0
- do behaviour chart for both vertical asymptotes
- max/min pt: avg of both VA, then plug that val into eqn
- domain and range (range is greater than HA and greater than/equal to max/min)
how to graph reciprocal of quadratic w/ no x-intercepts
- do VA, HA, x-int, y-int (will not have a VA)
- behaviour chart w/ just +-infinity
- domain is XER, range is greater than HA, less than or equal to max (y-int)
how to graph reciprocal of quadratic w/ one x-intercepts
- do VA, HA, x-int, and y-into **find y-int by plugging by doing f(0) and HA is y=0
- do behaviour chart for both vertical asymptotes
- max/min pt: avg of both VA, then plug that val into eqn
- domain and range (range is …)
solving eqns: fraction = fraction
cross multiply
solving eqns: fraction +- fraction = number
- common denom for fractions
- expand and simplify: move all to one side
- common factor
what should u NOT do when solving rational inequalities?
dont cross multiply
