APPC Unit 1A

Function

A mathematical relation that maps a set of input values to a set of output values such that each input value is mapped to exactly 1 output value

One

Each input has exactly _ output(s)

Domain

The set of input values of a function, represented by the independent variable (x)

Range

The set of output values of a function, represented by the dependent variable (y)

Positive function

When the graph of f lies above the x-axis / the outputs (y) are greater than 0

Negative function

When the graph of f lies below the x-axis / the outputs (y) are less than 0

Multiple Representations

Graphical, analytical, numerical, verbal

Increasing function

As the input values increase, the output values always increase

Decreasing function

As the input values increase, the output values always decrease

Concave Up

The rato of change is increasing

Concave down

The rate of change is decreasing

Point of inflection

Point where the graph changes concavity

instantaneous rate of change

the rate of change of a function at a point

rate of change of a function at a point

the rate at which the output values would change if the input values were to change at that point

AROC

the constant rate of change that yields the same change in the output values as the function yielded on that interval. The ratio of the change in the output values to the change in the input values over that interval

slope

rate of change is also called _____

linear

for any ____ function, the average rate of change over any length input value interval is constant

Linear

1st difference is the same

Quadratic

2nd difference is the same

concave up

the AROC over equal length input value intervals is increasing for all small length intervals

concave down

the AROC over equal length input value intervals is decreasing for all small length intervals

extrema

the minimums and maximums of a function

relative/local extrema

where the polynomial switches between decreasing and increasing

absolute/global extrema

the greatest of all local maxima/the least of all local minima

local

between 2 real zeros of a polynomial, there must be at least one _____ max or min

global

polynomials of EVEN degree must have a _____ max or min

point of inflection

occurs when a function changes from concave up to concave down or vise versa. Rate of change changes from increasing to decreasing or vise versa

degree

for a function to be a polynomial — the ____ cant be a variable or negative

degree

the multiplicity of a zero is the ___ of its factor

even

the graph of a polynomial will always be tangent to the x axis at any zero with an ____ multiplicity

bounce

an even degree means the graph will…

pairs

all imaginary roots come in…

fundamental theorem of algebra

a polynomial of degree n has exactly n complex zeros when counting multiplicities

even function

symmetric over the y axis + opposite inputs give the same outputs

odd function

symmetric over the x axis + opposite inputs give opposite outputs

end behavior

describes how a function behaves as it moves infinitely to the right and left

left behavior verbally

as the x values decrease without bound the y values of f(x)…

right behavior verbally

as the x values increase without bound the y values of f(x)…

left behavior limit statement

lim f(x) = ?

x → -oo

right behavior limit statement

lim f(x) = ?

x → oo

LS: down

RS: up

leading coeff : +

degree: odd

LS: up

RS: down

leading coeff: -

degree: odd

LS: up

RS: up

leading coeff: +

degree: even

LS: down

RS: down

leading coeff: -

degree: even