Elementary Algebra for College Students: Early Graphing, Second Edition

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Absolute value

The distance between that number and zero on the number line. When we find the absolute value of a number, we use the notation. To illustrate,

Absolute value inequalities

Inequalities that contain at least one absolute value expression.

Addend

When two or more numbers are added, the numbers being added are called addends. In the problem 3 + 4 = 7, the numbers 3 and 4 are both addends.

Additive identity element

0.

Additive inverses or opposites

For any number a, its additive inverse is -a.

Algebraic expression

An algebraic expression consists of variables, numerals, and operation signs.

Algebraic fraction

An expression of the form , where P and Q are polynomials and Q is not zero. Algebraic fractions are also called rational expressions. For example, are algebraic fractions.

Altitude of a geometric figure

The height of the geometric figure. In the three figures shown the altitude is labeled a.

Altitude of a triangle

The height of any given triangle. In the three triangles shown the altitude is labeled a.

Amount of a percent equation

The product we obtain when we multiply a percent times a number. In the equation 75 = 50% x 150, the amount is 75.

Approximate value

A value that is not exact. The approximate value of , correct to the nearest tenth, is 1.7. The symbol is used to indicate "is approximately equal to." We write

Area

The total surface area within a figure's boundaries.

Associative property of addition

The property that tells us that when three numbers are added, it does not matter which two numbers are added first. An example of the associative property is 5 + (1 + 2) = (5 + 1) + 2. Whether we add 1 + 2 and then add 5 to that, or add 5 + 1 and then add that result to 2, we will obtain the same result.

Associative property of multiplication

The property that tells us that when we multiply three numbers, it does not matter which two numbers we group together first to multiply; the result will be the same. An example of the associative property of multiplication is 2 x (5 x 3) = (2 x 5) x 3.

Asymptote

A line that a curve continues to approach but never actually touches. Often an asymptote is a helpful reference in making a sketch of a curve, such as a hyperbola.

Asymptotes of a hyperbola

Two lines through the center of the hyperbola that help in graphing the hyperbola.

Augmented matrix

A matrix derived from a linear system of equations. It consists of the coefficients of each variable in a linear system and the constants. The augmented matrix of the system is the matrix . Each row of the augmented matrix represents an equation of the system.

Axis of symmetry

The imaginary line about which a graph is symmetric.

Axis of symmetry of a parabola

A line passing through the focus and vertex of a parabola, about which the two sides of the parabola are symmetric. See the sketch.