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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 b0.

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...}