Unit 1 A Flashcards
if the leading coefficient is positive
open up, rise
if the leading coefficient is negative
open down, fall
if the leading degree is even
both ends will point in the same direction
if the leading degree is odd
both ends will point in opposite directions
relative/local extrema
where the function changes from increasing to decreasing (or vice versa) can be an endpoint – between two zeros there will be at least one
absolute/global extrema
the least or greatest y value of a function – can be an endpoint – all even degree polynomials will have one
points of inflection
where the graph changes from cu to cd
zeros are aka
x-ints, solutions, roots
multiplicity
the degree of the factor
odd multiplicity
cross
even multiplicity
bounce
complex numbers come in
pairs
fundamental theorem of algebra
if a polynoymial has a degree of x it will have x complex zeros
to solve nonlinear inequalities use
a sign chart
even functions are
symmetric with the y axis
odd functions are
symmetric about the origin
in even functions y(x)
is the same as y(-x)
in odd functions y(x)
is the opposite of -y(-x)
limits
lim f(x) = +/- inf as x –> +/- negative inf
to determine if something is a function use the…
vertical line test
domain
x-values, input, independent
range
y-values, output, dependent
function
a relation that maps a set of inputs onto a set of outputs such that each input has exactly one output
graph increasing
rising, positive slope, as inputs increase so do outputs
graph decreasing
falling, negative slope, as inputs increase outputs decrease
concave up
u, roc increasing
concave down
n, roc decreasing
slope equation
(y1-y2)/(x1-x2)
avg roc
slope between two points
inst roc
slope between two points that are REALLY close together
the roc of a linear function is…
constant
the roc of a quadratic function…
changes at a constant rate
