Need Statements

x-intercepts / zeros

y = 0 or f(x) = 0

y-intercepts

x = 0

y-axis symmetry / even function

f(-x )= f(x)

x-axis symmetry

-f(x) = f(x)

origin symmetry / odd fimctopm

f(-x) = -f(x)

parallel lines

m₁ = m₂

perpendicular lines

m₁ = -(1/m₂)

domain of √s(x)

s(x) ≥ 0

domain of ln[s(x)]

s(x) > 0

domain of 1 / s(x)

s(x) ≠ 0

intersection of f and g

f(x) = g(x)

rational functions zeros

numerator = 0

vertical asymptote

simplify, denom. = 0

lim (x→a^±) f(x) = ±∞

horizontal asymptote

degree num. = degree denom., ÷

lim (x→±∞) f(x) = a

x-axis asymptote

degree num < degree denom.

lim (x→±∞) f(x) = 0

slant asymptote

degree num, = 1 + degree denom., ÷

limit of a piece function

lim (x→a⁺) f(x) = lim (x→a−) f(x)

continuity at x=a

lim (x→a⁺) f(x) = f(a)

fundament theorem of calculus

∫(b, a) f(x)dx = F(a) + F(b), where F’(x) = f(x)

intermediate value theorem

f is continuous on [a, b]

k is between f(a) and f(b)

c exists, that f(c) = k

rolle’s theorem

f is cont. on [a, b]

f is diff. on (a, b)

f(a)=f(b)

c exits that f’(c) = 0

mean value theorm

f is cont. on [a, b]

f is diff. on (a, b)

c exists on (a, c) that

c = (f(b) - f(a)) / ( b- a )