Unit 1 AP Precalc

Relative Extrema

the local minimums and maximums of the graph

Absolute Extrema

the global maximum or minimum (most)

maximum: at 2(y), x = 3 (3,2)

If the line keeps going infinity on the ends,

there is no absolute minimum or maximum

Multiplicity

the amount of times the expression is multiplied by itself 

Even Function

opposite inputs give same outputs —→ (3,5) (-3,5)

Odd Functions

Opposite inputs give opposite outputs (-3, 5) (3,-5)

Big on Bottom

HA—> 0

Limit Statement ends in 0 

Same Degrees

Divide the coefficients for horizontal asymptote

Limit Statement equals HA 

Bigger on Top (more than one bigger)

no HA but divide coefficients

Limit Statement use infinity and negative infinity 

One more degree bigger

slant asymptote and divide rational expressions to fine

Limit Statement: use infinities 

X-intercept or zero

makes the numerator 0

Vertical Asymptote

when a factor in the denominator can’t cancel with the numerator

A hole/removable discontinuity

When a factor from denom. cancels with factor in the numerator

Limit Statement for hole as it approaches hole—>

the y value for the hole

Slant Asymptote

divide the rational expressions and remainders go over the divisor

Number line—> mark vertical, horizontal, and holes and shade corresponding to sign for 0

When dealing with bigger on top rational expressions..

Plug in the infinity signs to determine limit statement—> plug in for x from dividing leading coefficients