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# Express, Equa,&Funct

### Variables & Express

Term | Definition |
---|---|

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