Math Vocabulary Final
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76 terms
Terms | Definitions |
|---|---|
 Arithmetic Sequence | a sequence in which each term after the first is found by adding a constant, the common difference "d", to the previous term |
| Asymptote | a line that a graph approches |
| Change of base formula | for all positive numbers, "a", "b", "n", where a ≠ 1, b ≠ 1 Loga N= logbN/logbA |
| circle | the set of all points in a plane that are equidistant from a given point in the plane, called the center |
| Combined variation | when one quantity varies directly and/ or inversely as two or more other quantities |
| common difference | the difference between the successive terms of an arithmetic sequence |
| common logarithm | logarithms that use 10 as the base |
| common ratio | the ratio of successive terms of a geometric sequence |
| completing the square | a process used to make a quadratic expression into a perfect square trinomial |
| complex conjugates | two complex numbers of the form a+bi and a-bi |
| complex fraction | a rational expression whose numerator and/ or denominator contains a rational expression |
| complex number | any number that can be written in the form a+bi, where a and b are real numbers and i is the imaginary unit |
| composition of functions | a function is performed, and then a second fuction is performed on the result of the first function. The composition of f and g is denoted by f•g, and [f•g](x)= f[g(x)]. |
| compound inequality | two inequalities joined by the word "and" or "or" |
| conic section | any figure that can be obtained by slicing a double cone |
| consistent | a system of equation that has at least one solution |
| constant of variation | the constant k used with direct or inverse variation |
| continuous relation | a relation that can be graphed with a line or smooth curve |
| correlation coefficient | a measure that shows how well data are modeled by a linear equation |
| dependent | when a system of linear equations has an infinite number of solutions |
| dimensions of a matrix | the number of rows, m, and the number of columns, n, of the matrix written as m x n |
| direct variation | y varies directly as x if there is some nonzero constant k such that y=kx. k is called the constant of variation |
| discriminant | in the quadratic formula, the expression b^2 -4ac |
| ellipse | the set of all points in a plane such that the sum of the distances from two given points in the plane, called foci, is constant |
| end behavior | the behavior of the graph as x approaches positive infinity or negative infinity |
| exponential equation | an equation in which the variables occur as exponents |
| extraneous solution | a number that does not satisfy the original equation |
| extrema | the max and min values of a function |
| factor theorem | the binomial x-r is a factor of the polynomial P(x) if and only if P(r)=0 |
| Finite sequence | a sequence containing a limited number of terms |
| function | a relation in which each element of the domain is paired with exactly one element in the range |
| geometric sequence | a sequence in which each term after the first is found by multiplying the previous term by a constant r, called the common ratio |
| greatest integer function | a step function, written as f(x)=[[x]], where f(x) is the greatest integer less than or equal to x |
| growth factor | in exponential growth, the base of the exponential expression, 1+r |
| hyperbola | the set of all points in the plane such that the absolute value of the difference of the distances from two given points in the plane, called foci, is constant |
| identity function | the function I(x)=x |
| imaginary unit | i, or the principal square root of -1 |
| inconsistent | a system of equations that has no solutions |
| independent | when a system of linear equations has exactly one solution |
| infinite sequence | a sequence that continues without end |
| interval notation | a way to describe the solution set of an inequality |
| inverse function | two functions f and g are inverse functions iff both of their compositions are the identity function |
| inverse relation | two relations are inverse relations iff whenever one relation contains the element (a,b) the other relation contains the element (b,a) |
| inverse variation | y varies inversely as x if there is some nonzero constant k such that xy=k or y=k/x where x≠0 and y≠0 |
| joint variation | y varies jointly as x and z if there is some nonzero contant k such that y=kxz |
| latus rectum | the line segment through the focus of a parabola and perpendicular to the axis of symmetry |
| linear programming | the process of finding the max or min values of a function for a region defined by inequalities |
| logarithm | in the function x=b^y,y is called the log base b, of x. Usually written as y=〖log〗_b x and is read "y equals log base b of x" |
| logistic growth model | a growth model that represents growth that has a limiting factor. Logistic models are the most accurate models for representing population growth. |
| matrix | any rectangular array of variables or contants in horizontal rows and vertical columns |
| nth root | for any real numbers a and b and any positive integer n, if a^n =bthen a is an nth root of b |
| natural logarithm | logarithms with base e written lnx |
| negative exponent | for any real number a≠0 and any integer n, a^-n= 1/a^n and 1/a^-n= a^n |
| parabola | the graph of a quadratic function. The set of all points in a plane that are the same distance from a given point, called the focus, and a given line, called the directrix |
| parent function | the simplest most general function in a family of function |
| piece wise defined function | a function that is written using two or more expressions |
| point slope form | an equation in the form y-y1= m(x-x1) where (x1,y1) are the coordinates of a point on the line and m is the slope of a line |
| quadratic function | a function described by the equation f(x)= ax^2 +bx+c where a≠0 |
| radicand | in nth roots the value inside in the symbol √(n). Indicates the value that is being taken to the nth root |
| rate of change | how much a quantity changes on average relative to the change in another quantity over time |
| rational exponent | for any nonzero real number b, and any integers m and n, with except when b<0 and n is even |
| rational function | an equation of the form f(x)=p(x)/q(x) where p(x) and q(x) are polynomial functions and q(x)≠0 |
| rationalizing the denominator | to eliminate radicals from a denominator or fractions from a radicand |
| recursive formula | each term is formulated from one or more previous terms |
| regression line | a line of best fit |
| relative maximum | a point on the graph of a function where no other nearby points have a greater y coordinate |
| relative minimum | a point on the graph of a function where no other nearby points have a lesser y coordinate |
| root | the solutions of a quadratic equation |
| scatter plot | a set of data graphed as ordered pairs in a coordinate plane |
| sequence | a list of numbers in a particular order |
| set builder notation | the expression of the solution set of an inequality for example {xlx>0} |
| step function | a function whose graph is a series of line segments |
| synthetic division | a method used to divide a polynomial by a binomial |
| vertex form | a quadratic function in the form y= a(x-h)^2 +k where (h,k) is the vertex of the parabola and x=h is its axis of symmetry |
| vertical line test | if no vertical line intersects a graph in more than one point then the graph represents a function |
| zeros | the x intercepts of the graph of a function the points for which f(x) =0 |
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