Dictionary of Terms
Absolute value: The absolute value of a number is the distance from the number to zero on the real number line. The absolute value of a is denoted by |a|.
Adjacent side (to 
): The leg of a right triangle that touches the acute angle 
in question.
Arc length: The measure of an arc is called the arc length.
Arc: An arc is the portion of the circumference of a circle intercepted by a central angle.
Area: A measure of the space bounded by a 2-dimensional object.
Asymptote: An asymptote is a straight line on a graph that a curve approaches, but never meets. Asymptotes are classified as horizontal, vertical or oblique. Oblique means the line is neither horizontal nor vertical.
Base: The repeated factor in an exponential expression.
Base of a logarithm: This is the value of a in the following definition. If a and n are positive integers, then logan=k if and only if ak=n.
Base of an exponential expression: This is the value a in the notation an; it is the repeated factor.
Binomial: A binomial is a polynomial with exactly two terms. Example: 
Cartesian product: The Cartesian product of two sets A and B is denoted A ´ B and is the set of ordered pairs where the first coordinate is from A and the second is from B.
Central angle: An angle whose vertex is at the center of a circle.
Change of base formula: 
, where a, b, c >0.
Circumference: Circumference is the perimeter of a circle.
Coefficient: The coefficient of a term is the constant or numerical portion. Example: In the polynomial,
, we say the coefficient of 
is 3, the coefficient of 
is 1, the coefficient of 
is -5 and the coefficient of the constant term is 2.
Common denominator: A common denominator of two fractions is the least common multiple of the two denominators.
Complex number: A complex number is a number of the form a+bi, where a and b are real numbers and 
.
Composite number: A composite number is a whole number with more than two factors.
Continuous function: A continuous function is one whose graph has no holes and no jumps. The graph can be drawn without lifting the pencil off the paper.
Coordinate: One of the two numbers used to designate a point in the Cartesian graphing system. For example, 3 is the first coordinate of the point (3,5).
Coordinate axes: The two mutually perpendicular axes which split the Cartesian plane into fourths. A point in the plane is given coordinates based on the distance of the point from the axes.
Coterminal angles: These are angles which share a terminal side, when in standard position, such as 
and 
.
Critical point: The point at which a graph changes directions between up and down. In this graph, the critical points are circled:
Degree: In a polynomial function, the degree is the highest non-zero power of the independent variable in the function. For example, the polynomial
f (x)=3x4-5x2+7x+10 has degree 4.
Denominator: The denominator is the integer on the bottom of a fraction.
Dependent Variable: The dependent variable is the variable whose value depends on the other variable. For example, in the function 
, the y variable is the dependent variable, since its value is determined by the value given to the x variable. (To be more specific, if x = 2, then we know that y = 4. However, if y = 4, then it could be that x = 2 or that x = -2; we can’t be sure which.)
Difference: The result of a subtraction problem is called the difference.
Divides: Let 
and 
be two whole numbers, where 
. We say 
divides 
if and only if there exists a whole number 
such that 
. We write 
divides 
as 
.
Divisible by: Let x and y be two whole numbers, where y does not equal 0. We say y is divisible by x, if x divides y.
Divisor of: Let x and y be two whole numbers, where y does not equal 0. We say x is a divisor of y, if x divides y.
Domain: The domain of a function is the set of values taken by the independent variable.
e: A real number quantity defined by 
. It is frequently used as the base in functions modeling continuous exponential growth or decay.
Element: An element is a member of a set.
Empty set: The empty set is the set without any elements. It is written as 
.
Equation: An equation is two expressions connected by an equals sign. Example: 
Exponent: A positive integer exponent (like n in an) tells how many times the base appears as a factor.
Exponential function: This is a function of the form f(x)=b(ax), where a>0 and b is a real number. The quantity a is called the base of the function; b is the initial value.
Expression: An expression is a value that is represented by a combination of numbers and variables using mathematical operations such as addition, multiplication, roots, etc. A single variable or number is also considered an expression. Example: 
Factor: Let x and y be two whole numbers, where y does not equal 0. We say x is a factor of y, if x divides y.
Fraction: A fraction is a ratio of integers, 
where 
.
Function: A function is a relation, which assigns a unique value to the dependent variable (usually the y variable) for each value of the independent variable (usually the x variable). For example, the equation 
is a function, since there is exactly one y value for each x value. The equation 
is not, since there may be two different y values for one x value; for instance, when x = 4, y = 2 and y = -2.
Greatest common factor OR Greatest common divisor: Let x and y be two nonzero whole numbers. The greatest common factor of x and y is the largest whole number that is a factor of both x and y. This is written as gcf(x, y) or GCF(x, y). Some books use greatest common divisor instead of factor. This is written as gcd(x, y) or GCD(x, y).
Hypotenuse: The longest side of a right triangle; always opposite the right angle.
Improper fraction: An improper fraction is one where the numerator is larger than the denominator.
Independent variable: The independent variable is the variable whose value determines the value taken by the dependent variable. For example, in the function 
, the x variable is independent, since it determines the value taken by the y variable. (To be more specific, if x = 2, then we know that y = 4. However, if y = 4, then it could be that x = 2 or that x = -2; we can’t be sure which.)
Integer: The integers are the natural numbers, zero and the negatives of the natural numbers. Z = {...-3, -2, -1, 0, 1, 2, 3...}
Intercept: An intercept is where a graph intersects one of the two axes. The x-intercept(s) is where a graph intersects the x-axis, and the y-intercept(s) is where a graph intersects the y-axis. If an intercept is (a,0), we often just say that the x-intercept is a. Similarly, if a y-intercept is (0,b), we often say that the y-intercept is b.
Intersection: The intersection of sets A and B, written 
, is the set of all elements that A and B have in common.
Inverse function: Let 
be a one-to-one function. The inverse function is denoted 
where 
if and only if 
.
Irrational number: An irrational number is a number that cannot be written as a ratio of integers. An irrational number has a non-repeating and non-terminating decimal expansion.
Leading coefficient: The leading coefficient is the number, called a coefficient, which is multiplies the highest non-zero power of the independent variable in a polynomial function. For example, the polynomial 
has 3 as its leading coefficient.
Least common multiple: Let x and y be two nonzero whole numbers. The least common multiple of x and y is the smallest whole number that is a multiple of both x and y. This is written as lcm(x, y) or LCM(x,y).
Logarithmic function: This is a function of the form g(x)=b(logax), where a>0 and b is a real number.
Major axis of ellipse: This is the longer axis of an ellipse.
Minor axis of ellipse: This is the shorter axis of an ellipse.
Mixed number: A mixed number refers to an improper fraction which is written with an integer and a fractional part.
Monomial: A monomial is a polynomial with a single term. Examples: 
, 
, 
and 7
Multiple: Let x and y be two whole numbers where y does not equal 0. We say y is a multiple of x, if x divides y.
Natural number: The natural numbers are the counting numbers. N = {1, 2, 3, 4, 5, 6...}
Numerator: The numerator is the integer on the top of a fraction.
One-to-one function: A function is one-to-one if each element in the range corresponds to exactly one element in the domain.
Opposite side (to 
): The leg of a right triangle that does not touch the acute angle 
in question.
Origin: The origin is the point where the x- and y-axes cross each other, and is assigned the coordinates (0,0).
Parabola: A parabola is the graph associated with a quadratic function, i.e. a function of the form 
.
Perimeter: The distance around the exterior of a 2-dimensional object is the perimeter.
Point: A point is a specific place on a graph given by specific coordinates, e.g. (3,5).
Polynomial: A polynomial is any function of the form
f (x) = anxn + an-1xn-1 + … + a1x + a0.
Prime factorization: Every composite number can be written as a product of prime numbers. This is called the prime factorization of a number.
Prime number: A prime number is a whole number with exactly two factors.
Product: The result of a multiplication problem is called the product.
Proper subset: Set B is a proper subset of set A if and only if every element in B is an element of A and A contains at least one element that is not in B. This is denoted by 
.
Proportion: A proportion is an equation in which two ratios are set equal to each other.
Quadrantal angle: This is an angle where the terminal side is coincident with a coordinate axis, such as 
or 
.
Quadrant: The coordinate axes divide the Cartesian plane into four sections; these are called the quadrants of the plane and numbered I, II, III, IV. In quadrant I, both the x and y coordinates are positive; the numbering continues in a counterclockwise fashion.
Quadratic: Quadratic is another way of saying a polynomial of degree 2. Example: 
Quotient: The result of a division problem is called the quotient.
Radian: A radian is a unit of angle measure; a central angle of 1 radian intercepts an arc of measure 1 unit on a unit circle.
Range: The range of a function is the set of values taken by the dependent variable.
Ratio: A ratio is an ordered pair of numbers a and b, written a:b where b
0.
Rational number: If a number can be written as a ratio of integers, then it is called a rational number. A rational number has either a repeating or finite decimal expansion. Q is used to denote the set of rational numbers.
Real number: The set of real numbers is the union of the set of rational numbers and the set of irrational numbers. R is used to denote the set of real numbers.
Reciprocal: The reciprocal of a number a, where a 0, is denoted by 
, and is the number such that 
.
Reciprocal function: This is a function of the form 
.
Reference angle: If 
is an angle in standard position, the terminal side of 
and the x-axis make an acute angle 
in standard position; this angle 
is the reference angle for 
.
Reference triangle: A reference triangle is a right triangle containing a reference angle as one of its vertices; used to compute trigonometric function values of an angle in standard position.
Root: A root of a polynomial 
is a value for the variable which solves the equation 
. Example: Let 
. 
has roots 
and 
.
Set: A set is a collection of objects.
Slope: The slope is the measure of the steepness of a straight line; the change in its y coordinates divided by the change in its x coordinates. Its equation is normally represented as 
, where 
and 
are points on the line. The slope of a vertical line is undefined.
Straight angle: A straight angle measures 
radians or 
.
Subset: Set B is a subset of set A if and only if every element of B is also an element of A. This is denoted 
.
Sum: The result of an addition problem is called the sum.
Surface area: A measure of the space on the exterior of a 3-dimensional object.
Symmetry: A graph is said to have “_____ symmetry” if it would remain unchanged under some translation, rotation, or reflection. For example, these two graphs have symmetry:
Trigonometric identities: These are equalities involving trigonometric functions; often used to simplify equations.
Union: The union of sets A and B, written 
, is the set of all elements contained in A or contained in B.
Unit circle: The unit circle is a circle of radius 1 with center at the origin.
Vertex: The vertex is the unique critical point on a parabola. Here is a parabola with its vertex labeled: 
Volume: A measure of the amount of space contained within a 3-dimensional object.
Whole number: The whole numbers are the natural numbers and zero. {0, 1, 2, 3, 4, 5...}