AP Calculus BC - Test #1 (Ch. 1-3)CORRECT 100%

AP Calculus BC - Test #1 (Ch. 1-
3)CORRECT 100%
given absolute value in formula: what should you do? - ANSWERwrite out separate
parts; test +/- using number line method; write out as a *piecewise*

the upper or lower half of a parabola [ex: x = √(y)] - ANSWERthe lower half is usually
the negative part of ±, and vise versa

when changing/altering a function, how does the domain change? - ANSWERthe
domain is restricted to the original domain

if a function is one-to-one, or x is in the range of f/the domain of f⁻¹ -
ANSWERƒ(ƒ⁻¹(x)) = x

sin(arcsin(x)) = x when - ANSWERx is [-1,1] → domain of inside function

cos(arccos(x)) = x when - ANSWERx is [-1,1] → domain of inside function

arcsin(sin(x)) = x when - ANSWERx is [−π/2, π/2] → domain of inside function (to fit
outside too)

arccos(cos(x)) = x when - ANSWERx is [0, π] → domain of inside function (to fit
outside too)

tan(arctan(x)) = x when - ANSWERx is [-∞, ∞] → domain of inside function

tan(arctan(x)) = x when - ANSWERx is [

domain & range: sinx - ANSWERD: all real
R: [-1, 1]

domain & range: cosx - ANSWERD: all real
R: [-1, 1]

domain & range: tanx - ANSWERD: only no asymptotes
R: all real

domain & range: cotx - ANSWERD: only no asymptotes
R: all real

domain & range: arcsinx - ANSWERD: [-1, 1]
R: [−π/2, π/2]

Squeeze Theorem - ANSWERif ƒ(x)≤g(x)≤h(x) when x is near a AND lim x→a ƒ(x) =
lim x→a h(x) = L, then lim x→a g(x) = L