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algebra
| Question | Answer |
|---|---|
| absolute value | the distance from the number to zero on a number line Example: |3| = 3 or |-3| = 3 |
| absoute value function | a function written in the vertex form f(x) = a |x – h| + k, where a ≠ 0; the graph of an absolute value function is a “V” shape |
| asymptote | a line that a curved graph gets closer to without every touching |
| at least | must be more than |
| axis of symmetry | for a quadratic function, a vertical line that includes the vertex of a quadratic function resulting in the two sides of the graph look like mirror images of each other |
| base | in a logarithm, the base is the number that is raised to a power If nx = a, the logarithm of a, n is the base. |
| binomial | a polynomial with two terms Examples: (x - 2) or (3x + 5) |
| change of base formula | To change a logarithmic expression with base b to a common log (base 10), use the formula: logb (ARGUMENT) = log (ARGUMENT) log b |
| circle | the locus of points that are a fixed distance from a given point |
| coefficient | the number multiplied times a product of variables or powers of variables in a term |
| completing the square | a method of symbolic manipulation in which a polynomial can be rewritten to include a binomial that is squared |
| complex number | a number of the form a + bi where a and b are real numbers, and b ≠ 0 |
| compound monthly | when interest is earned not only on the original principal but also on the accumulated interest of prior months |
| constant | a term or expression with no variables; a value that does not change |
| continuous | a set of points without breaks |
| degree | the highest exponent in an equation |
| dependent variable | a variable (usually “y”) whose value is found by using the value of the independent variable (usually “x”) |
| depreciates | losing value over time |
| discontinuities | places on the graph of a function where two pieces are separated by a jump, hole, or an asymptote |
| discrete | a set of individual points |
| distributive property | a property of real numbers that states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products x(a + b) = ax + bx |
| domain | the set of input values of a function or relation |
| equation | a mathematical sentence that equates two expressions; an equation contains an equal sign, = |
| exponent | says how many times to use the number in a multiplication In this example: 82 = 8 × 8 = 64 or x2 = x × x. |
| exponential | a function where the variable is the exponent of a constant base |
| exponential decay | for f(x) = a * Bx+c + d, if a > 0 and 0 < B < 1, then the y-values decrease (or decay) as the x-values increase The rate of decay is proportional to the y-value, so as the y-values get smaller, the graph flattens out (or approaches a horizontal asymptote |
| exponential growth | for f(x) = a * Bx+c + d, if a > 0 and B > 1, then the y-values increase (or grow) as the x-values increase The rate of decay is proportional to the y-value, so as the y-values get larger, the graph grows without bound (or exponentially). |
| expression | a mathematical sentence that shows a relationship among real numbers and variables; an expression does not contain a symbol implying equality or inequality |
| extraneous roots | a solution of a modified equation that is NOT a solution to the original equation |
| dxtraneous solution | a solution of a modified equation that is NOT a solution to the original equation |
| function | a fixed point on the interior of a parabola The distance from the focus to the parabola is equal to the distance from the directrix to the parabola. |
| holes | points where the graph of a function does not exist |
| horizontal asymptote | a line that a graph approaches more and more closely |
| horizontal shift | movement of a graph to the right or left A function f(x) can be moved “h” units right/left by performing the operation f(x ± h). |
| imaginary number | a value that includes the square root of a negative number |
| imaginary root | A quadratic equation is said to have imaginary roots when the quadratic formula yields imaginary or non-real answers. Also, the graph of a function with imaginary roots will not touch the x-axis. |
| independent variable | the input of a function (usually “x”) whose value is used to find the value of the dependent variable (usually “y”), values can be freely chosen |
| index of a radical | the nth root of x where n is the index is represented by the radical; radical √x has an index of 2 and is often called the square root of x |
| inequality | a number sentence where one quantity can be greater or less than another quantity, a number sentences with inequality symbols |
| infinitely many solutions | a system in which there are an infinite number of ordered pairs that satisfy all of the equations; also referred to as a dependent system |
| infinity | going on forever, of not having an end, of having no boundary |
| integer | the set of positive and negative whole numbers {…-2, -1, 0, 1, 2 …} |
| inverse of a function | a function obtained by exchanging the input and output values of a one-to-one function |
| inverse | a function that undoes what the original function did |
| irrational number | a number that cannot be written in fractional form, a non-terminating (does not end) and non-repeating decimal value, examples include all non-perfect square roots (√2, √3, etc. and π) |
| logarithm | a power to which a base, [actually 10] must be raised to produce a given number If nx = a, the logarithm of a, with n as the base, is x. |
| logarithmic function | function written in the simple base form y = logB(x) These functions can be rewritten without logarithms in the equivalent statement: x = By Only positive real numbers have real logarithms. You cannot take the logarithm of a negative number. |
| max value | the highest point on the graph of the quadratic function |
| min value | the lowest point on the graph of the quadratic function |
| multiplying binomials | Use the FOIL method to multiply binomials. |
| no solution | when there isn’t any value that will make the equation true |
| parabola | a U-shaped curve that is the graph of a quadratic function |
| parent function | the simplest function for a family of functions |
| piecewise | a function that is a combination of pieces of two or more other functions |
| polynomial | an expression with one or more terms containing variables, real numbers, or products of one or more variables and a real number with whole-number exponents |
| polynomial form | an equation that is written as a polynomial; y = ax2 + bx + c is the polynomial form of a quadratic equation |
| quadratric | a second degree equation, which can be written in general form y = Ax2 + Bx + C |
| Quadratic expression/quadratic function | a polynomial function whose highest exponent is 2; the graph is a parabola The general form is: f(x) = ax2 + bx + c. |
| quadratic formula | the formula which gives solutions or roots for equations of the form ax2 + bx + c (a ≠ 0) |
| radical | a root of a quantity, e Example: √x |
| radicand | the number or expression under a radical sign |
| range | the set of values of the dependent variable for which a function is defined |
| rational function | the quotient of two polynomials where the denominator has a degree greater than zero In other words, there needs to be a variable in the denominator to be a rational function |
| rational number | any number that can be expressed as a ratio (fraction) |
| real number | every point on the number line; can be either a rational or irrational number |
| roots | the solution(s) of a quadratic equation |
| square | to raise a number or expression to the 2nd power |
| square root function | a function whose rule contains a variable beneath a square-root sign |
| solution | roots, zeros, x-intercepts, or values where the function equals zero |
| standard form | a quadratic equation written in the form: y = ax2 + bx + c, where a ≠ 0 |
| trinomial | a polynomial with three terms |
| variable | usually) letters or other symbols representing unknown numbers or values |
| vertex | for a quadratic function, the lowest (minimum) or the highest (maximum) point on the graph |
| vertex form | y= a(x – h)2 + k, where a, h, and k are constants and (h,k) is the vertex of the parabola |
| vertical asymptote | a line that a graph approaches more and more closely |
| vertical shift | movement of a graph up or down A function f(x) can be moved “k” units up/down by performing the operation f(x) ± k. |
| x-int | the point(s) where the function crosses the x - axis |
| y-int | the point(s) where the function crosses the y - axis |
| zero product property | If ab = 0, then a = 0 or b = 0 Example: If (x + 1)(x + 2) = 0, then (x + 1) = 0 or (x + 2) = 0. |
| zeros | the solution(s) of a quadratic equation; a value of x that makes a function f(x) equal to 0, a zero of a function may be real or imaginary |
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