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function

If you repeat an INPUT, and you always get the same OUTPUT, your data is a ______________________ .

Relation

A Smart Art graphic type that compares connections between concepts.

graph of the function

The set of all points x, y that forms a graph in the xy-plane.

x-value (x-coordinate)

the first number in an ordered pair

Input

the first coordinate of an ordered pair in a relation (x,y)

independent variable

the tested varaible

y-value (y coordinate)

the second number in an ordered pair

Output

the second coordinate of an ordered pair in a relation (y in x, y)

dependent variable

the measure of change in the independent variable

(-2,-2) (2,-1) (3,0) (5,3) (5,4)

No, this relation is not a function because the ordered pair (5,3) and (5,4) have the same input but different outputs.

(-3,-1) (-2,0) (-1,3) (-1,0) (0,-1)

No, this relation is not a function because the ordered pair (-1,3) and (-1,0) have the same input but different outputs.

(4,11) (5,18) (6,25) (7,32) (8,39)

Yes, this relation is a function because every input has exactly one output.

(10,1) (11,6) (12,11) (13,16)(14,21)

Yes, this relation is a function because every input has exactly one output.

(0,1) (1,2) (2,3) (3,4) (4,4)

Yes, this relation is a function because every input has exactly one output.

Domain

The ______________________ is all the possible INPUT, X, values.

Range

The difference between the greatest number and the least number in a set of data.

increasing function

Interval along the domain

Decreasing function

Interval along the domain

x-intercept

the point where the line crosses the x-axis

y-intercept

the point where the line crosses the y-axis

Function test

Vertical line test - only 1 point of function on each vertical line.

Function notation

In general, a special numerical relationship where the symbol f(x) replaces y and is read as "the value of f at x" or simply as "f of x".

Interval notation

2 lines with Parentheses and brackets

reflection

It is a transformation that flips a figure over a line of reflection.

Horizontal

Straight line across from side to side (length)

vertical

The direction of something that runs north to south or south to north.

Maximum

the highest possible y value for the graph of a quadratic function; also the y-coordinate of the vertex

Minimum

the lowest possible y value for the graph of a quadratic function; also the y -coordinate of the vertex

Vertical shift

# is outside ( ) that is added or subtracted

Horizontal shift

# is inside ( ) that is being added or subtracted.

Function getting narrower

Mult by whole #

Function getting wider

Multiplying by a fraction/decimal

Quadratic Function

a function that can be written in the form f(x)=ax^2+bx+c, where a, b & c are real numbers and a is not equal to zero

Linear Function

y = mx + b

Absolute value functiom

Graph is in the shape of a v

Exponential Function

y = ab^x

Discrete

is a quantitative variable that is usually a count such as 0, 1, 2, 3

Continuous

is a quantitative variable that has a continuum of infinitely many possible values

functional notation

f(x) where f is the function and x is the input; read "f of x"

evaluation

substitute and simplify; plug and chug

Absolute Value Function

any f(x) = | x |

square root function

a function that contains the independent variable in the radicand

four function families

linear, quadratic, absolute value and square root

graph

A visual display of data

VERTICAL LINE TEST

A line is a function is it passes the

Algebra is...

... the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics.

Variable

an alphabetic character representing a number, called the value, which is either arbitrary or not fully specified or unknown. It is usually a letter like x or y.

Equation

A mathematical sentence that contains an equals sign

slope

(y₂-y₁)/(x₂-x₁)

constant

a value that does not change in an expression

substitute

To replace a variable with a number or another expression in an algebraic expression.

simplify

find an answer in its simplest form. example 2 +3 can be simplified to 5

Coordinate Graph

A picture of a relationship using one axis for each variable.

origin

The centre point of a number line (ground floor of a hotel, freezing point on a thermometer)

x-axis

The horizontal axis on a coordinate plane.

y-axis

The vertical axis on a coordinate plane.

coordinates

Are used to pinpoint where you are on a map or graph. They are also referred to as or Cartesian coordinates.

parallel lines

2 lines that never cross/intersect and stay the same distance apart

Perpendicular lines

lines in a plane that intersect to form 4 right angles

Parabola

the graph of a quadratic function

vertex

The point where two sides meet. (Shared end points of the line segments of a polygon.)

set notation

an indication that a group of numbers is part of a set

i

the set of all positive x and y coordinates lie in this quadrant

IV

the set of all positive x and negative y coordinates lie in this quadrant

III

the set of all negative x and y coordinates lie in this quadrant

II

the set of all negative x and positive y coordinates lie in this quadrant

straight line

the graph of a linear equation is a...

x

for every coordinate, this variable comes first

y

for every coordinate, this variable comes second

f(x) means...

f is a function of x

y

f(x) is a fancy way of saying...

How do you make a function table?

choose appropriate values for x, and find f(x) for each value

Continuous Data

Data can take on any values in the domain of the variable; usually measurements of something

Discrete Data

A list-able set of values; usually counts of items

2(5) = 10

If f(x) = 2x, what is f(5)?