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Functions


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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)?