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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^±
Note
Flashcard