Y'all Flashcards
asymptotes
a line that graph approaches but never intersects
discontinuity:
function is not defines at that point, graph has a break (ex. reciprocal function)
complete the square:
a way to factor expressions from standard tov vertex form
inverse: switch x and y
vertex:
the max/min of a quadratic function
linear function standard form:
ax + by + c=0
quick things from standard form
where x-int: -c/a, yint: -c/b and m= -a/b
reflections:
y=-a is reflection in x-axis while y=4(-x)… is reflection in y-axis
when saying what variables affect what, please include reflections
things to remember unit 1:
numbers on graph, use variables given, x-lies, mas value is not max point, arrows on graph, let statements, plus and minus when square rooted
point symmetry:
when the points can be flipped and still land on the function (ex. linear function)
line symmetry:
when the function cana be flipped along an axis and fal back on itself (ex. absolute value)
rational numbers
can’t have “0” on bottom
restrictions:
on denominator (original) as things may simplify but without restrictions, the two graphs are not equivalent
holes:
when something cancels out at the top and bottom
va:
restrictions of denominator
things to remember unit 2:
functions always have “f(x)”, circle the exponent,
discriminant:
when it is greater than 0= 2 different roots with 2 x-intercepts and 2 zeroes. when it is equal to zero= 2 equal, real and distinct roots, 1 x-int, 1 zero. when less than 0= 2 complex distinct roots, 0 x-ints, 0 zeroes.
things to remember unit 3:
no silly mistakes, check eqns in calculator
things to remember unit 4:
asymptote must be a dotted line on graph, must indicate if thing is growing or decaying.
principle angle:
measured counterclockwise from x (clockwise if –ve)
terminal arm:
hypoteneuse of triangle
co-terminal angles:
angles that land on same terminal arm (30=390=-330 etc.)
related acute angle:
acute angle near origin (beta angle?)
cosine law:
used for sas, sss triangles
speed of a wave:
2”pie”r/period
things to remember unit 5
side lengths can be –ve, leave things exact,
discrete function:
defined only for a set of numbers that can be listen (graph has pointsm dotted line, no arrows)
things to remember unit 6:
don’t add and subtract, please multiply and divide, check your answer by doing the sequence. you can use the summation button to find values
recursive formula:
when the pattern is based on the term before it. neither arithmetic nor geometric (most of the time). domain is t1=___ then n must be greater than ____.
don’t mess dis stuff up or pushed will not be your mom
move negative sign off of denominator, answer the question! check domain of inverses carefully, be careful about logs and if possible, graph it to check, can’t do trig ratios on not right angle triangles! Units! degrees!
compound interest formula
used for repaying/investing all at once
annuity
when you have no money and plan to make money
present value of an annuity
when you are repaying loans or spending savings (slowly)
when a function is undefined
it is most likely a horizontal/vertical asymptote,
trig identities
please state restrictions
real life application of domain and range
see start and end points, use the variables given
how many answers does a non special triangle always have?
2
LET STATEMENTS
OK
when to use a=p(1+i)^n
Use this when the questions says “compounded” and you are looking for how much something will be worth in teh future. There is only one loan or deposit. i.e. If you deposit $5000 in a bank account that earns 4.5%/a interest compounded monthly, how much will you have in 10 years? There is only 1 deposit of $5000, and you’re looking for how much it will be worth in the future.
P=principle
A=future amount
i= interest rate (decimal)
n= # of compounds/year
When to use A= r[(1+i)^n-1]/i
(Annuity) Use this for repeated deposits (saving money). i.e. If you deposit $100 each month into a savings account, how much will you have after 3 years if interest is 3%/a compounded monthly. Use annuity because its repeated deposits of $100.
pv= R[1-(1+i)^-n]/i
(Annuity) Use this for repeated payments (paying off a loan) i.e. If you make $300 car payments each month and you pay %3/a interest compounded monthly, how much was the car worth when you bought it? There are repeated payments and you want to know what the loan was worth (in the past so negative n).
annuity vs compound interest
check for “withdrawals” or “payments”
exponents
check if they are in our out of brackets
PV = A(1 + i )^-n
Use this when its compound ineterest but you want to know how much it was worth in the past. If you want to have $5000 in your bank account in 10 years, what should you deposit now if your account earns 4.5%/a interest compounded monthly? There is only one deposit happening now and you want to know what that deposit was now (the past) if it will be $5000 in the future.
