15.2 词汇表(F-O)

章节大纲

• 选择节常规

  折叠 展开

  常规

  全部折叠 展开全部

  • 选择活动新闻通告

    

    新闻通告 讨论区
• 选择节词汇(F-O)

  折叠 展开

  词汇(F-O)

  播放段落

  F
  ::F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F F

  factor

  Factors are numbers or expressions being multiplied to equal a product. To factor means to rewrite a mathematical expression as a product of factors.

  Factor Theorem

  Given $\begin{align*}f(x)\end{align*}$ , a polynomial of degree $\begin{align*}n>0\end{align*}$ , $\begin{align*}f(c)=0\end{align*}$  if and only if $\begin{align*}x-c\end{align*}$  is a factor of the polynomial $\begin{align*}f(x)\end{align*}$ .

  factored completely

  An algebraic expression is factored completely when it is a product of prime factors.

  factorial

  The factorial of a whole number $\begin{align*}n\end{align*}$  is the product of the positive integers from 1 to $\begin{align*}n\end{align*}$ . The symbol "!" denotes factorial.  $\begin{align*}n! = 1 \cdot 2 \cdot 3 \cdot 4...\cdot (n-1) \cdot n. \end{align*}$
  

  factoring by grouping

  An algebraic technique by which you collect terms that have a greatest common factor (GCF) in groups, and then factor out the GCF from just those terms.

  feasible region

  The region of a graph where all the solutions of a system of linear inequalities overlap.

  Fibonacci sequence

  A sequence in which the next number in the sequence is determined by adding the previous two terms. The 1st terms of the sequence are 1, 1, 2, 3, 5, 8, 13….

  finite

  A set that has a limited number of elements is called a finite set.

  finite sequence

  A sequence with a finite number of terms.

  foci

  Multiple reference points for a conic section.

  focus

  A reference point for a conic section.

  FOIL

  An acronym used to remember a technique for multiplying two binomials. You multiply the FIRST terms, OUTSIDE terms, INSIDE terms, and LAST terms, and then combine any like terms.

  formula

  A type of equation that shows the relationship between different variables.

  fractional expression

  An expression in which any algebraic expression is divided by any algebraic expression.

  function

  A relation in which there is only one output for every input. In other words, for every value of $\begin{align*}x,\end{align*}$  there is only one value for $\begin{align*}y.\end{align*}$
  

  function notation

  A shorthand notation that allows us to name functions.

  Fundamental Theorem of Algebra

  If $\begin{align*}f(x)\end{align*}$  is a polynomial of degree $\begin{align*}n\ge 1\end{align*}$ , then $\begin{align*}f(x)\end{align*}$  has at least one zero in the complex number domain. In other words, there is at least one complex number $\begin{align*}c,\end{align*}$  such that

  $\begin{align*}f(c)=0\end{align*}$ . The theorem can also be stated as follows: An $\begin{align*}{n}^{th}\end{align*}$ -degree polynomial with real or complex coefficients has, with multiplicity, exactly $\begin{align*}n\end{align*}$  complex roots.

  Fundamental Theorem of Arithmetic

  Every positive integer is either a prime number or a composite number, which can be expressed as a unique product of prime numbers. Note this means that the prime factorization of each composite number is unique.

  播放段落

  G
  ::G 级

  general form of a quadratic function

    $\begin{align*}f(x) = a{x}^{2} + bx + c,\end{align*}$  where $\begin{align*}a,b,\end{align*}$  and $\begin{align*}c\end{align*}$  are real numbers and $\begin{align*}a\neq 0\end{align*}$ .

  general form of the equation of a line

  $\begin{align*}Ax+By=C,\end{align*}$  where $\begin{align*}A,B,\end{align*}$  and $\begin{align*}C\end{align*}$  are real numbers.

  generator

  A line drawn at an angle to an axis that we rotate 360 degrees to form a double right-circular cone.

  geometric sequence

  A sequence with a constant ratio between successive terms. Also known as a geometric progression.

  global maximum/minimum

  The global extrema (maximum/minimum) of a function are the points with the $\begin{align*}y\end{align*}$ -values that are the highest or lowest of the entire function.

  graph

  Pictures of all the solutions to an equation.

  graphing

  The process of drawing a graph.

  greatest common factor

  The greatest common factor of two numbers or variable expressions is the greatest number or expression that all the original expressions can be divided by evenly.

  growth factor

  The amount the exponential function grows by, $\begin{align*}1+r\end{align*}$ . Populations and interest commonly use growth factors.

  播放段落

  H
  ::赫 时

  half-life

  The time required for a radioactive material to decay to one-half its initial concentration.

  horizontal asymptote

  A horizontal line that indicates the end behavior of a function as the independent variable gets very large or very small. A function may touch or pass through a horizontal asymptote.

  horizontal line test

  If a horizontal line drawn anywhere through the graph of a function intersects the function in more than one location, then the function is not one-to-one.

  hyperbola

  A conic section formed when the cutting plane intersects both sides of the cone.

  播放段落

  I
  ::一一

  identity property

  If a number is operated with the additive or multiplicative identities in addition or multiplication respectively, then the result is the number itself. For example:  $\begin{align*}a+0=a\end{align*}$ , $\begin{align*}a\cdot 1=a\end{align*}$ . 

  imaginary part

  The imaginary part of a complex number $\begin{align*}a + bi\end{align*}$  is $\begin{align*}bi\end{align*}$ .

  improper fraction

  A fraction in which the absolute value of the numerator is greater than the absolute value of the denominator.

  inconsistent system

  A system of equations is inconsistent if it has no solutions.

  increasing

  A function is increasing over an interval if its $\begin{align*}y\end{align*}$ -values are getting larger over the interval. The graph will go up from left to right over the interval.

  independent system

  A system of equations is independent if no two equations coincide.

  independent variable

  The input variable in an equation or function, commonly represented by $\begin{align*}x\end{align*}$ .

  index

  Part of the radical that indicates which root to calculate.

  index of summation

  This part of a summation tells us what terms to add.

  inequality

  A mathematical statement that relates expressions that are not necessarily equal by using an inequality symbol. The inequality symbols are $\begin{align*}<,>,\le ,\ge ,\neq \end{align*}$ .

  infinite

  A set with an unlimited number of elements.

  infinite sequence

  A sequence with an infinite number of terms.

  infinite series

  The sum of the terms in a sequence that has an infinite number of terms.

  integers

  All natural numbers, their opposites, and zero. Integers are numbers in the list ... -3, -2, -1, 0, 1, 2, 3....

  intercept

  The locations where a curve intersects the $\begin{align*}x\end{align*}$  and $\begin{align*}y\end{align*}$  axes. An $\begin{align*}x\end{align*}$ -intercept is a point at which the curve intersects the $\begin{align*}x\end{align*}$ -axis. A  $\begin{align*}y\end{align*}$ -intercept is a point at which the curve intersects  the $\begin{align*}y\end{align*}$ -axis.

  interest

  A percentage of lent or borrowed money. Interest is calculated and accrued regularly at a specified rate.

  intersection

  The intersection of two sets is the set that contains elements that are in both sets, indicated it with $\begin{align*}\cap.\end{align*}$  The operation of intersection is associated with the logical term AND.

  interval

  An interval on the number line is a connected set of numbers.

  interval notation

  A notation that uses the endpoints to indicate the smallest and largest values in the interval—and we assume that all numbers in between them are included. Use ( or ) to indicate the end value is not included, and [ or ] to indicate the end value is included.

  inverse function

  Inverse functions are functions that "undo" each other. Formally,  $\begin{align*}f(x)\end{align*}$  and $\begin{align*}g(x)\end{align*}$  are inverse functions if $\begin{align*}f(g(x))=g(f(x))=x\end{align*}$ .

  inverse operation

  Inverse operations are operations that "undo" each other. Multiplication is the inverse operation of division. Addition is the inverse operation of subtraction.

  inverse property

  If a number is operated with the additive or multiplicative inverses in addition or multiplication respectively, then the result is the additive or mutiplicative identity. For example, $\begin{align*}a + (\text{-}a) = 0\end{align*}$ , $\begin{align*}a \cdot \frac{1}{a} = 1\end{align*}$ .

  inverse variation

  A relationship between two variables in which the product of the two variables is equal to a constant. As one variable increases, the 2nd variable decreases proportionally.

  irrational numbers

  When written as a decimal, these numbers do not terminate or repeat.

  播放段落

  J
  ::J J

  joint variation

  Variables exhibit joint variation if one variable varies directly as the product of two or more other variables.

  播放段落

  K
  ::K K 级

  播放段落

  L
  ::L L L

  latus rectum

  The line segment perpendicular to the axis of symmetry that goes through the focus. The endpoints of the line segment are points on the parabola.

  leading coefficient

  In a polynomial, this is the coefficient of the variable with the highest degree.

  leading term

  In a polynomial, this the term that contains the variable with the highest degree.

  least common denominator (LCD)

  The LCD of two fractions is the smallest number or expression that is a multiple of both the original denominators. It is the least common multiple (LCM) of the denominators.

  least common multiple (LCM)

  The LCM of two numbers is the smallest number that is a multiple of both of the original numbers.

  like terms

  Terms that are composed of the same variables with the same exponents on each variable.

  line of best fit

  The line of best fit on a scatterplot is a drawn line that best represents the trend of the data.

  linear equation

  An equation that can be written in the form $\begin{align*}ax+b=c\end{align*}$ , where $\begin{align*}a,b, \end{align*}$  and $\begin{align*}c\end{align*}$  are real numbers.

  linear inequality

  An inequality that can be written in one of the following four forms: $\begin{align*}ax+b>c,ax+b<c, ax + b \ge c, \end{align*}$  or $\begin{align*}ax+b\le c\end{align*}$ .

  linear programming

  Using the vertices of the feasible region (the area of overlap between multiple inequalities) to determine a maximum or minimum value.

  linear regression

  In statistics, a process that attempts to model the relationship between two variables by fitting a linear equation to the data.

  literal equation

  An equation that contains letters or literals, what we call variables.

  local maximum/minimum

  The local extrema of a function are the points of the function with $\begin{align*}y\end{align*}$ -values that are the highest or lowest of a local neighborhood of the function.

  logarithm

  The inverse of an exponential function, which is written $\begin{align*}\log_b a = x,\end{align*}$  such that $\begin{align*}{b}^{x} = a\end{align*}$ .

  logarithmic form

  $\begin{align*}\log_b a = x\end{align*}$ , such that $\begin{align*}b\end{align*}$  is the base.

  lower nappe

  The surface of the lower cone in a double right-circular cone.

  播放段落

  M
  ::M 男

  major axis

  The longer of the two axes that pass through the center of an ellipse.

  mathematical expression

  A mathematical phrase containing variables, operations, and/or numbers. Expressions do not include comparative operators, such as equal signs or inequality symbols.

  maximum

  The highest point of a graph. The maximum will yield the largest value of the range.

  minimum

  The lowest point of a graph. The minimum will yield the smallest value of the range.

  minor axis

  The shorter axis that passes through the center of an ellipse.

  mixed number

  A number made up of a whole number and a proper fraction, such as $\begin{align*}4\frac{3}{5}.\end{align*}$
  

  model

  A mathematical expression or function used to describe a physical item or situation.

  monomial

  A polynomial with only one term.

  multi-step equation

  An algebraic equation that requires multiple steps to solve.

  multi-step inequalities

  An algebraic inequality that requires multiple steps to solve.

  multiple

  A multiple of a number is the product of that number and a whole number.

  multiplication property of equality

  If the same constant is multiplied to both sides of the equation, the equality holds true.

  multiplication property of inequality

  When an inequality is multiplied by a negative number, the sense of the inequality changes and the sign is reversed.

  multiplicative identity

  1 is the multiplicative identity.

  multiplicative inverse

  $\begin{align*}\frac{1}{a}\end{align*}$  is the multiplicative inverse of a.

  multiplicity

  The number of times that a given term acts as a zero of the given function.

  播放段落

  N
  ::N 内

  nappe

  The surface of a double right-circular cone.

  natural logarithm

  A log with base $\begin{align*}e\end{align*}$ . The natural logarithm is written as $\begin{align*}ln.\end{align*}$  

  natural numbers

  The counting numbers, consisting of all positive, whole numbers. The natural numbers are the numbers in the list 1, 2, 3,... and are often referred to as positive integers.

  negative correlation

  A negative correlation appears as a recognizable line with a negative slope.

  no correlation

  If the points of a scatter plot have no sort of linear pattern.

  non-rigid transformation

  A transformation that distorts the original shape of the graph.

  null set

  A set with no elements.

  播放段落

  O
  ::OO

  objective function

  A function for the quantity we are trying to maximize or minimize in a linear programming problem.

  oblique asymptote

  A diagonal line marking a specific range of values toward which the graph of a function may approach, but generally never reach. An oblique asymptote exists when the numerator of the function is exactly one degree greater than the denominator. An oblique asymptote may be found through long division.

  octant

  Any one of the eight "corners" of the three-dimensional rectangular coordinate system.

  one-step equation

  An algebraic equation with one operation in it that requires one step to solve.

  one-step inequality

  An algebraic inequality that requires one step to solve.

  one-to-one

  A one-to-one function is a function in which each output corresponds to a unique input. Formally, if $\begin{align*}f({x}_{1})= f({x}_{2})\end{align*}$ , then $\begin{align*}{x}_{1} ={x}_{2}\end{align*}$ .

  open interval

  An interval in which the endpoints are not included.

  order of operations

  The order in which to perform each of multiple operations in an expression or equation. The order of operations is: P – parentheses, E – exponents, M/D – multiplication and division, in order from left to right, A/S – addition and subtraction, in order from left to right.

  ordered pair

  An ordered pair, $\begin{align*}(x,y)\end{align*}$ , describes the location of a point on a coordinate grid.

  ordinate

  The $\begin{align*}y\end{align*}$ -coordinate of the ordered pair that represents a plotted point on a Cartesian plane. For the point (3, 7), 7 is the ordinate.

  origin

  The point of intersection of the $\begin{align*}x\end{align*}$  and $\begin{align*}y\end{align*}$  axes on the Cartesian plane. The coordinates of the origin are (0, 0).