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Terms in this set (58)
Interval
An interval is a portion of a number line
Interval notation
Notation used to indicate an interval on the number line
Inequality
Statement with algebraic expressions related by <,>
Linear inequality in one variable
A linear inequality in the variable x can be written in the for ax+b < c
Equivalent inequality
Inequalities with the same solution set
Intersection
The intersection of two sets a and b is the set of elements that belong to both a and b
Compound inequality
Formed by joining two inequalities with a connective word such as and or or
Union
The union of two sets a and b is the set of elements that belong to either a or b
Absolute value equations / inequalities
Absolute value equations and inequalities are equations and inequalities that involve the absolute value of a variable expression
Ordered pair
An ordered pair is a pair of numbers written in parentheses in which the order of the number is important
Origin
When two number lines intersect at a right angle, the origin is the common 0 point with coordinates (0,0)
X-axis
Horizontal number line in a rectangle coordinate system is called the y-axis
Y-axis
Vertical number line in a rectangle coordinate system is called the x-axis
Rectangular (Cartesian) coordinate system
Two number lines that intersect at a right angle at their 0 points
Plot
To plot an ordered pair is to locate it on a rectangular coordinate system
Components
The two numbers in an ordered pair are the components of the ordered pair
Coordinate
Each number in an ordered pair are the components of the ordered pairs
Quadrant
A quadrant is one of the four regions in the plane determined by a rectangular coordinate system
Graph of an equation
The graph of an equation is the set of points corresponding to all ordered pairs that satisfy the equation
First-degree equation
A first-degree equation has no term with a variable to a power rather than one
Linear equations in two variables
A first-degree equation with two variables is a linear equations in two variables
X-intercept
Point where a line intersects the x-axis
Y-intercept
Point where a line intersects the y-axis
Rise
Rise of a line is the vertical change between two points on the line
Run
Run of a line is the horizontal change between two points on the line
Slope
Ratio of the change in y compared to the change in (use/run) along a line is the slope of the line
boundary lines
In the graph of a linear inequality, the boundary line separates the region that satisfies the inequality from the region that does not satisfy the inequality
Dependent variable
If the quantity y depends on x, then y is called the dependent variable in a relation between x and y
Independent variable
If y depends on x, then x is the independent variable in a relation between x and y
Relation
A relation is a set of ordered pairs of real numbers
Function
A function is a set of ordered pairs in which each value of the first component, x, corresponds to exactly one value of the second component, y.
Domain
The domain of a relation is the set of first components (x- values)
Range
The range of a relation is the set of second component (y-values)
Function notation
The function notation f(x) is another way to represent the dependent variable y for the function f
Linear function
A function that is defined by f(x) =mx + b is a linear function
Constant function
Constant function is a linear function in the form f(x) = b, for a real number b
System of equations
Two or more equations that are to be solved at the same time form a system of equations
Linear system
System of equations that contains only linear equations
Solution set of a system
All ordered pairs that satisfy all the equations of a system at the same time make up the solution set of a system
Consistent system
Is consistent if it has a solution
Independent equations
Equations whose graphs are different lines
Inconsistent system
Inconsistent if it has no solution
Dependent equations
Equations whose graphs are the same line
Matrix
A matrix is a rectangular array of numbers, consisting of horizontal rows and vertical columns
Elements of a matrix
Numbers in a matrix are its elements
Square matrix
Matrix that has the same number of rows and columns
Augmented matrix
An augmented matrix is a matrix that has a vertical bar that separates the columns of the attic into two groups
Row echelon form
If a matrix is written with 1s down the diagonal from upper left to lower right is below the 1s, is said to be in row echelon form
Elements of a matrix
...
Consistent system
...
System of equations
Two or more equations that are to be solved at the same time form a system of equations
Linear system
...
System of equations
...
System of equations
Two or more equations that are to be solved at the same time form a system of equations
Constant function
...
Y-intercept
Point where a line intersects the y-axis
Rise
...
Y-intercept
...
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