AP Precalc 2.1-2.3 Quiz

Arithmetic sequence equation

A_n= A₀ +dn

what does a₀ stand for in an arithmetic sequence

the 0th term in the sequence

how to find the o term in the sequence

subtract the first term by the common difference

what does d stand for in an arithmetic sequence

common difference

arithmetic sequence equation when given a term

a_n=a_k+d(n-k

geometric sequence equation

a_n=a₀ x (R) ^x

if the sequence is being divided by a factor of two what if your common ratio

1/2

Geometirc sequuence equation when given the kth term

a_n= a_k ( r) ^n-k

arithmetic sequences are

linear

geometric sequences are

exponential

over equal length intervals, the if the output values change at a constant rate, then the function is

linear/ arithmetic

over equal length intervals, the if the output values change proportionally then the function is

exponential/ geometric

equation of a function given it is linear

f(x)=d(x-x₁)+y₁

equation of a function given it is exponential

f(x)= y₁ ( r )^x-x₁

if the exponential function has an a value greater then zero is it above or below the x axis

above

if an exponential function has a a value less then 0 is it above or below the x axis

below

if an exponential function has a b values that is greater then 1 and the a value is greater than 0 is it growing or decaying

growing

if an exponential function has a b values that is in between 0 and 1 and the a value is greater than zero is it growing or decaying

decaying

if an exponential function has a b values that is in between 0 and 1 and the a value is less than zero is it growing or decaying

growing/ increasing

if an exponential function has a b values that is greater than 1 and the a value is less than zero is it growing or decaying

decreasing/ decaying

a function has an a value greater than 0 and a b value greater than 1 what is the limit as x approaches positive infinity

positive infinity

a function has an a value greater than 0 and a b value greater than 1 what is the limit as x approaches negative infinity

0

a function has an a value greater than 0 and a b value between 0 and 1 what is the limit as x approaches positive infinity

0

a function has an a value greater than 0 and a b value between 0 and 1 what is the limit as x approaches negative infinity

positive infinity

a function has an a value less than 0 and a b value between 0 and 1 what is the limit as x approaches positive infinity

0

a function has an a value less than 0 and a b value between 0 and 1 what is the limit as x approaches negative infinity

negative infinity

a function has an a value less than 0 and a b value greater than 1 what is the limit as x approaches positive infinity

negative infinity

a function has an a value less than 0 and a b value between 0 and 1 what is the limit as x approaches negative infinity nfinity

0

functions with an a value greater than 0 are always going to have what rate

increasing rate (concave up)

functions with an a value less than 0 are always going to have what rate

decrease rate (concave down)

if the output values of g are proportional over equal length imput value intervals then g is

exponental

proportional means

multipling by some number to get the next thing

to find if the values in an arithmetic sequence are going to be greater than the values in a geometric sequence

DRAW IT OUT

match up the exponential terms to the linear terms that are the same and see if the term you are looking for is greater than less than or equal to the other!

what is the general term of a sequence

the sequence with the 0 term

(distribute the common differnece with n and k)

if you are given the percent value that is lost or gaine what should you do

add or subtract it from 100!

how to know when to use functions or secquences

functions are continuous (includes decimals aka you would need it)

Sequences are discrete (specific numbers like 1, 2,3 use when trying to find like the number of plants cost or smth)

if you are given the translation of a function, how do you know if it is or is not proportional

try adding the transformation to a set of exponential numbers (2,4,8) to see if you still end up with a common ratio

if you do a vertical translation to an exponential function, the output values will not be

PROPORTIONAL

how do you find the initial value of an exponential function

plug 0 in as the exponent (should get your y-value

what is the base on an exponential function

the common ratio