Pre-Requisites Flashcards
Slope is a ___ ___ between x and y increments.
constant ratio
In a linear equation, equal increments in the ___ ___ correspond to equal increments in the ___ ___.
independent variable, dependent variable
Increment
Change in a variable
Implied domain
When no restrictions are given to a function, the domain is assumed to be the largest set of x-values for which the formula gives real y values.
Even function
f(-x) = f(x), symmetric about the y-axis
Odd function
f(-x) = -f(x), symmetric about the origin
Compound interest formula
P(1 + r/n)^nt, principal P, annual interest rate r compounds n times per year t
Continuously Compounded Interest
Pe^rt, an account begins with principal P and earns annual interest r compounded continuously
Half-life
A(t) = P(1/2)^t/h, the amount of material present at time t, where h is the half-life
e
As n approaches infinity, (1 + 1/x)^x
Identity Function
f(g(x)) = g(f(x))
a^log_a(x) where x,a>0, a doesn’t equal 1
x
log_a(a^x), a>0 for all x
x
log_a(xy)
log_a(x) + log_a(y)
log_a(x/y)
log_a(x) - log_a(y)