precalc unit 1 review

even function

f(-x) = f(x)

odd function

f(-x) = -f(x)

end behavior of a positive even function

as x reaches -infinity f(x) reaches infinity

as x reaches infinity f(x) reaches infinity

end behavior of a negative even function

as x reaches -infinity f(x) reaches -infinity

as x reaches infinity f(x) reaches -infinity

end behavior of a positive odd function

as x reaches -infinity f(x) reaches -infinity

as x reaches infinity f(x) reaches infinity

end behavior of a negative odd function

as x reaches -infinity f(x) reaches infinity

as x reaches infinity f(x) reaches -infinity

domain of a rational function

when x ≠ 0

HA limit notation

lim f(x) = HA

x → ± infinity

HA if numerator < denominator

HA = 0

HA if numerator > denominator

no HA, long/synthetic division for slant asymptote

HA if numerator = denominator

HA = leading coefficients

When is there a hole in a function?

If a zero is at both numerator and denominator

When is a zero in a function?

When there’s a zero in the numerator only

When is there a VA in a function?

When there’s a zero in the denominator only

VA limit notation

lim f(x) = ± infinity

x → VA^±

^+ = from the right

^- = from the left

Limit notation for holes

lim f(x) = y-value hole is at

x → x-value hole is at^±