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)
log_a(x)^y
ylog_a(x)
For a function to have an inverse
Each output is associated with an input
Domain if log_a(x)
Range of a^x, (0, infinity)
Range of log_a(x)
Domain of a^x, (-infinity, infinity)
Domain, range, period of y = tanx
D: x doesn’t equal kpi/2, k is an odd integer
R: (-infinity, infinity)
P: pi
Domain, range, and period of y = secx
D: x doesn’t equal kpi/2, k is an odd integer
R: (-infinity, -1]U[1, infinity)
Period: 2pi
Domain, range, and period of y = cscx
D: x doesn’t equal npi, n is an integer
R: (-infinity, -1]U[1, infinity)
P: 2pi
Domain, range, and period of y = cotx
D: x doesn’t equal npi, n is any integer
R: (-infinity, infinity)
P: pi
Domain and range of cos^-1(x)
D: [-1, 1]
R: [0, pi]
Domain and range of y = sin^-1(x)
D: [-1, 1]
R: [-pi/2, pi/2]
Domain and range of tan^-1(x)
D: (-infinity, infinity)
R: (-pi/2, pi/2)
Domain and range of sec^-1(x)
D: (-infinity, -1]U[1, infinity)
R: [0, pi], y doesn’t equal pi/2
Domain and range of csc^-1(x)
D: (-infinity, -1]U[1, infinity)
R: [-pi/2, pi/2], y doesn’t equal 0
Domain and range of y = cot^-1(x)
D: (-infinity, infinity)
R: (0, pi)
