how to solve system of equations
graphically
- calc, intersection
elimination
substitution
discrete vs contiuous
continuous - graphed as liine or curve
discrete - graphed as separate discrete points
piecewise function
has 2 or more equations for diff intervals of the domain of the function
vertex from standard form
-b/2a
vertex from vertex form
(h,k)
relation
set of ordered pairs
verticle line test
used to determine if graph is a function
composite functions
function of a function
fog = gof?
no
inverse
swap x and y
solve
put back into function notation
domain and range are switched
horizontal line test
to see whether functions have an inverse
rational functions
2 symmetrical branches
a/(x-h) + k
(ax+b)/(cx+d)
asymptotes
horizontal - a/c (y) - range
Vertical - set denominator = 0 - domain
one to one function
whe each value of domain is assigned to a distinct value in the range
how to prove that 2 functions are inverse of each other
do the composite functions of each, if answers are both x, then they are inverses
to find where two inverse functions intersect… trick
intersect one with the y=x line
F (x) = a
F-1 (a) = x
when given composite function (fog)(x) and inverse do (f^-1)(x)
f(x) = F^-1((fog)(x))
