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Express, Equa,&Funct

Variables & Express

TermDefinition
algebraic expression an expression consisting of one or more numbers and variables along with one or more arithmetic operation OR consist of sums and/or products of numbers and variables
variable symbols used to represent unspecified numbers or values
term a number, a variable, or a product or quotient of numbers and variables
factor in an algebraic expression, the quantities being multiplied
product in an algebraic expression, the result of quantities being multiplied
power an expression of the form x^n, read x to the nth _____ - refers to exponent
exponent in an expression of the form x^n, the _________ is n. It indicates the number of times x is used as a factor
base in an expression of the form x^n, the _____ is x
evaluate to find the value of an expression
order of operation 1) Evaluate expressions inside grouping symbols 2) Evaluate all powers 3) Do all multiplication's and/or divisions from left to right 4) Do all additions and/or subtractions from left to right
like terms are terms that contain the same variables, with corresponding variables having the same power
simplest form an expression when it contains no like terms or parentheses
coefficient a term is the numerical factor
Distributive Property that the product of a number and a sum is equal to the sum of the individual products of the addends and the number. That is, a(b + c) = ab + ac.
equivalent expressions equations that denote the same value for all values of the variable (ex. 4k + 8k = 12k)
additive identity for any number a, a+0=0+a=a- the sum of any number and 0 is equal to the number
multiplicative identity for any number a, a*1=1*a=a -the product of any number and 1 will equal
multiplicative property of zero the solution of the equation is 0. The product of any number and 0 is equal to 0. (6*m=0)
multiplicative inverses of reciprocals two numbers whose product is 1 or reciprocals
commutative property 2+4=4+2
associative property the sum or product is to group the numbers together ex. (a+b) +c = a + (b+c) for addition and multiplication
open sentence a mathematical statement with one or more variable OR a mathematical statement that contains the algebraic expression and symbols
equation a mathematical sentence that contains an equals sign, =
solving finding a value for a variable that makes a sentence true
solution the replacement value for the variable in an open sentence
replacement set a set of numbers from which replacement for a variable may be chosen
set is a collection of objects or numbers that is often shown using braces
element each object or number in the set or member OR each entry in a matrix)
solution set is a set of elements from the replacement set that make an open sentence true
identify an equation that is true for every value of the variable
coordinate system the grid formed by the intersection of two number lines, the horizontal axis and the vertical axis
x-axis the horizontal number line on a coordinate plane ( horizontal axis)
y-axis the vertical number line on a coordinate plane (vertical axis)
coordinate plane the plane containing the x-axes and the y-axes
origin the point where the two axes intersect at their zero points (0,0)
ordered pair a set of numbers or coordinates used to locate any point on a coordinate plane, written in the form (x,y)
x- coordinate the first number in an ordered pair (represent the horizontal point)
y- coordinate the second number in an ordered pair (represents the vertical point)
relation a set of ordered pairs
mapping illustrates how each element of the domain is paired with an element in the range
domain the set of the first numbers of the ordered pairs in a relation
range 1) the set of second numbers of the ordered pairs in a relation
independent variable the variable in a function with a value that is subject choice (determines the output)
dependent variable the variable in a relation with a value that depends on the value of the independent variables
function is a relationship between input and output OR a relationship in which each element of the domain is paired with exactly one element of the range
discrete function a graph that consists of points that are not connected
continuous function a function graphed with a line or smooth curve
vertical line test used to see if a graph represents a function OR if any vertical line passes through no more than one point of the graph of a relation, then the relation is a function
function notation equations that are functions can be written in a form OR a way to name a function that is defined by an equation. In function notation, the equation y=3*8 is written as f(x)= 3x-8
nonlinear function a function with a graph that is not a straight line
intercepts of a graph are points where the graph intersects an axis
y-intercept the y-coordinate of a point where a graph crosses the y-axis
x-intercepts the x-coordinate of a point where a graph crosses the x-axis
line symmetry in the y-axis or some other vertical line if each half of the graph on either side of the line matches exactly
positive a function is positive on a portion on its domain where its graph lies above the x-axis
negative a function is negative on a portion of its domain where its graph lies below the x-axis
relative minimum point A is this since no other nearby points have a lesser y-coordinate
relative maximum point B is this side no other nearby points have a greater y-coordinate
extrema the point shown are the locations of relatively high or low function values
increasing the graph of a function goes up on a portion of its domain when viewed from left to right
decreasing the graph of a function goes down on a portion of its domain when viewed from left to right
end behavior describes how the values of a function behave at each end of the graph OR describes the values of a function at the positive and negative extremes in its domain
Created by: erica.kercher