**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 *log _{a}n=k* if and only if

*a*.

^{k}=n**Base of an exponential expression:** This is the value *a* in the notation *a ^{n}*; 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*)=3x^{4}-5x^{2}+7*x*+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(a ^{x})*, 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(log _{a}x), *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*) = a_{n}x^{n} + a_{n-1}x^{n-1 }+ … + a_{1}x + a_{0}.

**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...}