calc theories

absolute value rules/reminders

• flip sign when dividing by -

• |a|≤n → -n≤a≤n

• plug condition to test if number needs to be multiplied by -1 because a+x must be positive

rationalizing

multiply fraction by denominator/denominator but if there are any signs (±) flip them

determining continuity

1. direct sub into f(x) → f(a) to determine if the function is defined. if undefined (0/0), it is discontinuous

2. lim x→a f(x) exists at x=a (factor, solve, you get a number)

3. f(x)=lim x→a, continuity

f(x) at a undefined but lim x→a exists, what type of discontinuity

hole

if lim x → a^- ≠ lim x → a⁺

jump

if lim = n/0

vertical asymptote

root function

_{———————->}
(

sqrt(x)

polynomial function

U
ax²+bx+c

rational function

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__/ \__ f(x)/g(x)