APPC Unit 1B

rational function

the quotient (fraction) of two polynomials

0

what can the denominator never equal for a rational function

end behavior

____ of a rational function is determined by the leading terms of the numerator and denominator

y = a/b

the leading terms have the same degreen

y = 0

the denominator dominates the numerator

no HA

the numerator dominates the denominator

a/b

end behavior for same degree

0

end behavior for denominator > numerator

(a/b)x^(n-d)

end behavior for numerator > denominator ((behaves like))

Hint: -oo / oo

slant/oblique

if the degree of the numerator is exactly 1 more than the degree of the denominator, then f(x) has a _____ asymptote that is PARALLEL to the leading terms (a/b)x^(n-d)

zeros

when the numerator = 0

vertical asymptotes

when the denominator = 0 (undefined)

zeros; undefined values

when solving rational inequalities, we need to identify BOTH the _____ and ______ (VA)

brackets; parenthesis

______ for zeros when "≤" or "≥"; and ____ for zeros when < or > and for VAs when <, >, ≤ , or ≥

restrictions

when dividing by a polynomial, rational functions have _____ on their domain

0

vertical asymptotes and holes both occur when the denominator of a rational function equals…

hole

occurs when the factor in the DENOMINATOR cancels our with factors in the numerator

vertical asymptote

occurs when a factor in the denominator CANNOT cancel out with factors in the numerator

substitute

to find the y-value of a hole, ___ x with the x-value of the hole in the “new equation”

limit statements

all end behaviors are _______ but not all are end behaviors

hole

lim f(x) → n

x → n-/+

VA

lim f(x) = -/+ oo

x → n-/+

end behavior

lim f(x) → n

x → -/+ oo

check

when writing an equation of a rational function and using a hole…

same

even power = approaching in ___ direction

hole; VA

____ and ___ affect the domain

long division

to find the equation of a slant asymptote, use ____

y = mx + b

equation of a slant

degree

the row of Pascal’s triangle corresponds to the ____ of the binomial

0

Pascal’s triangle starts on row…

Pascal’s triangle

used for expanding expressions of the form (a-b)^n

alternate

when expanding binomials, if there is a negative in the middle, the signs will…

vertical translation

g(x) = f(x) ± k

horizontal translation

g(x) = f(x ± h)

vertical dilation

g(x) = ±af(x)

x-axis

if a < 0, f is reflected over the….

horizontal dilation

g(x) = f(±bx)

y-axis

if b < 0, f is reflected over the…

inside

any transformatiosn that occur ___ the parenthesis will affect the x-values

opposite

transformations will do the ____ of what it looks like to the x-values

same

transformation will do ____ what it looks like to the y-values

outside

transformations that affect the y-values wil occur ___ the parenthesis