Idea South Flores Algebra 1 Terms

Infinite Series

A series that has no last term, such as . The sum of an infinite series is defined as the limit of the sequence of partial sums.

y-intercept

A point at which a graph intersects the y-axis

Variable

A quantity that can change or that may take on different values. Variable also refers to a letter or symbol representing such a quantity.

Function

A relation for which each element of the domain corresponds to exactly one element of the range. For example, is a function because each number x in the domain has only one possible square root. On the other hand, is not a function because there are two possible values for any positive value of x.

No Slope

The "slope" of a vertical line. A vertical line has undefined slope because all points on the line have the same x-coordinate. As a result the formula used for slope has a denominator of 0, which makes the slope undefined..

x-intercept

A point at which a graph intersects the x-axis. The x-intercepts of a function must be real numbers, unlike roots and zeros

Equation

A mathematical sentence built from expressions using one or more equal signs (=).

Slope of a Line

A number which is used to indicate the steepness of a line, as well as indicating whether the line is tilted uphill or downhill. Slope is indicated by the letter m.

Linear System of Equations

A system of equations in which each equation is linear. **For any linear system, exactly one of the following will be true: There is only one solution, there are infinitely many solutions (consistent), or there are no solutions (inconsistent). A linear system with more equations than variables is called over determined, and a linear system with more variables than equations is called under determined.

Zero of a Function

A value of x which makes a function f(x) equal 0. A zero may be real or complex

Real Numbers

All numbers on the number line. This includes (but is not limited to) positives and negatives, integers and rational numbers, square roots, cube roots , π (pi), etc.

Linear Equation

An equation that can be written in the form "linear polynomial = linear polynomial" or "linear polynomial = constant". The following are examples of linear equations: 2x - 3 = 5, 4a + 9 = 8 - 9a, and 2x + 5y = 1.

Linear Inequality

An inequality that can be written in the form "linear polynomial > linear polynomial" or "linear polynomial > constant". The > sign may be replaced by <, ≤, or ≥. The following are examples of linear inequalities: 2x - 3 < 5, 4a + 9 ≥ 8 - 9a, and 2x + 5y ≤ 1.

Solution Solution Set

Any and all value(s) of the variable(s) that satisfies an equation, inequality, system of equations, or system of inequalities. With a system of equations or system of inequalities, the solution set is the set containing value(s) of the variable(s) that satisfy all equations and/or inequalities in the system.

Inequality

Definition 1: Any of the symbols <, >, ≤, or ≥. Definition 2: A mathematical sentence built from expressions using one or more of the symbols <, >, ≤, or ≥.

Recursive Formula

For a sequence a1, a2, a3, . . . , an, . . . a recursive formula is a formula that requires the computation of all previous terms in order to find the value of an .

Graph of an Equation or Inequality

If there is only one variable, the graph is on a number line. If there are two variables, the graph is on the coordinate plane. If there are three variables, the graph is in three-dimensional coordinates. In general, for n variables, the graph is in n dimensions.

Linear

Like a line. A description of any graph or data that can be modeled by a linear polynomial

Coordinates Ordered Pair Ordered Triple n-tuple

On the coordinate plane, the pair of numbers giving the location of a point (ordered pair). In three-dimensional coordinates, the triple of numbers giving the location of a point (ordered triple). In n-dimensional space, a sequence of n numbers written in parentheses.

Coordinate Plane Cartesian Plane

The plane formed by a horizontal axis and a vertical axis, often labeled the x-axis and y-axis, respectively.

Domain

The set of values of the independent variable(s) for which a function or relation is defined. Typically, this is the set of x-values that give rise to real y-values.

System of Equations

Two or more equations containing common variable(s).

System of Inequalities

Two or more inequalities containing common variable(s). Note: Systems of inequalities sometimes include equations as well as inequalities.