Algebra 2

a^m * aⁿ=

a^m+n

(a^m)ⁿ=

a^mn

(ab)^m=

a^mb^m

a^m/aⁿ=

a^m-n, a cannot equal 0

State the domain and range for the function f(x)=x^1/2

D: [0,infinity)

R: [-infinity, infinity)

What is the equation for an exponential growth model?

y = a(1+r)^t

What is the equation for an exponential decay model?

y = a(1-r)^t

What is the asymptote, domain, and range of the function f(x) = 2^x

HA: y = 0

D: (-infinity, infinity)

R: [0, infinity)

What is the asymptote, domain, and range of the function f(x) = log₂x

VA: x = 0

D: [0, infinity)

R: (-infinity, infinity)

log_bmn =

log_bm + log_bn

log_b(m/n) =

log_bm - log_bn

log_bmⁿ =

nlog_bm

What transformations were made: f(x) → f(x-h)

right h

What transformations were made: f(x) → f(x) + k

up k

What transformations were made: f(x) → -f(x)

reflection over the x-axis

What is the formula for an explicit arithmetic sequence?

a_n = a₁ + d(n-1)

What is the formula for a recursive arithmetic sequence?

a_n = a_n-1 + d

a₁ = …

What is the formula for an explicit geometric sequence?

a_n = (a₁)r^n-1

What is the formula for a recursive geometric sequence?

a_n = r(a_n-1)

a₁ = …

sin²x + cos²x =

1

cot²x+1 =

csc²x

tan²x + 1 =

sec²x

What is the period of a sine or cosine graph?

2pi/b

What is the period of a tangent graph?

pi/b

What is the theoretical P(A)?

number of favorable outcomes/total number of outcomes

P(A and B) =

P(A) * P(B)

ONLY IF INDEPENDENT

P(B l A) =

P(A and B)/P(A)

P(A or B) =

P(A) + P(B) - P(A and B)

What are the percentages for standard deviation?

34%, 13.5%, 2.35%, 0.15%

What is the formula for the margin of error with standard deviation?

plus/minus 1/sqrtn

(n = sample size)

What is the formula for interest that is compounded daily/monthly/yearly/etc?

A = P(1+r/n)^nt

What is the formula for interest that is compounded continuously?

A = Pe^rt