toolkit functions,

Constant Graph: f(x)=c where c is a constant

identity graph f(x)=x

absolute value

quadratic

cubic f(x)= x^3

reciprocal f(x)= 1/x

reciprocal squared f(x)=1/x^2

Square root

cube root

function define

- a characteristic

-an example

-a nonexample

a rule for a relationship between an input and an output where each input value determines a unique one output value. the output is a function of the input

f(input)=output. CAN ONLY HAVE ONE INPUT BUT CAN HAVE SAME OUTPUTS

characteristic: f(x)

example: parabola, y=mx+b, inverse function

nonexample: circle

relation

A set of ordered pairs (x,y)

x and y names

x- input, domain, independent variable

y- output, range, dependent variable

one to one function define

Sometimes in a relationship each input corresponds to exactly one output, and every output corresponds to exactly one input. We call this kind of relationship a one-to-one function.

The notation y=f(x) defines a function named f. This is read as

"y is a function of x."

USE VERTICAL line test to see if its a

function

use vertical and horizontal line tests to see if its a

one to one function

Domain:

Range:

Domain: The set of possible input values to a function Range: The set of possible output values of a function

x is less than a

( -infinity, a)

x is greater than a

(a, infinity)

x is greater than or equal to a

bracket a, infinity)

x is less than or equal to a

(-infinity, a bracket

a less than x less than b

(a, b)

years vs, students domain and range

bracket 2011, 2018 bracket

range: curly least to greatest curly

piecewise-defined function

f(x)= curly .10x if domain

Using a square bracket [ means the start value is blanked in the set Using a parenthesis ( means the start value is blanked in the se

included, not included

Average rate of change = Change of Input/ Change of Output =

y2-y1/x2-x1

A function is increasing on an interval if....

More formally, a function is increasing if f(b) > f(a) for any two input values a and b in the interval with b>a. The average rate of change of an increasing function is blank.

the function values increase as the inputs increase.

positive

A function is decreasing on an interval if ....

More formally, a function is decreasing if f(b) < f(a) for any two input values a and b in the interval with b>a. The average rate of change of a decreasing function is blank .

the function values decrease as the inputs increase.

negative

A point where a function changes from increasing to decreasing is called a ....

local maximum

A point where a function changes from decreasing to increasing is called a ....

local minimum.

Together, local maxima and minima are called the blank blank, or local extreme values, of the function

local extrema

closed circle =

closed bracket

open cirlce =

open parenthesis

write the range using interval notation how

closed bracket look on y axis closed bracket

what is the domain of f(x)= 3 square root x-2

x is greater than or equal to 2

-can't take sqrt of negative number

domain of 3x+1/4x+2

{x/x triton R, x cannot equal -1/2}

domain of square rt of x+4/ x-4

{x/x greater than or equal to -4, x cannot equal 4}

solve vs evaluate graph

solve f(x)=4

evaluate f(2)

find 2 on x axis and move up

solve: find 4 on y axis and move side to side