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64 Cards in this Set
- Front
- Back
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relation
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Any pairing between two groups. Each item in each group must be paired, so there are no leftover items.
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domain
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In a relation, elements of the first group, or input group.
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range
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In a relation, elements of the second group, or output group.
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function
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A relation in which each domain element is paired exactly once with a domain element.
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vertical line test
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A relation is a function when any vertical line crosses the graph of the relation exactly once.
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All functions are relations…
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but not all relations are functions.
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The function notation f(x) = 2x is read… and means...
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“A function in x” equals two x” or more simply “F of x equals 2x”, and means that every value of the domain is multiplied by two to yield a value in the range.
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There does/does not have to be a rule or equation that connects the domain to the range.
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does not
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Notation: If (3, -5) is a point on a graph, then f(3) =
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-5
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A square root function looks like…
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a half parabola, opening sideways.
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An absolute value function looks like…
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a V-shape.
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A linear function looks like…
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a line, which could be horizontal, rising, or falling, but not vertical.
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A quadratic (squartic) function looks like…
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a U shape, or parabola.
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A half parabola, opening sideways is…
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a square root function.
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A V-shape is the graph of…
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an absolute value function.
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A line is the graph of a…
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linear function.
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A parabola or U-shape is the graph of a…
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quadratic (squartic) function.
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A piecewise defined function…
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has a rule or equation for each section of the function.
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A translation is…
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a transformation that shifts the graph up, down, left, or right.
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A vertical translation is achieved when…
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something is added or subtracted as the LAST operation on the variable. Adding shifts up, subtracting shifts down.
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A horizontal translation is achieved when…
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something is added or subtracted as the FIRST operation on the variable. Adding shifts left, subtracting shifts right.
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A reflection is…
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a transformation that is a mirror image of the graph across a line.
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Stretch/compress/reflection is achieved by…
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the leading coefficient of the function.
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Reflection is achieved by…
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changing the sign of the leading coefficient of the function.
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Stretch is achieved by…
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changing the leading coefficient of the function to a number farther away from zero than 1.
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Compress is achieved by…
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changing the leading coefficient of the function to a number between 0 and 1.
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For polynomial functions, stretch and compress are always…
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vertical, not horizontal.
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It’s a polynomial function when…
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the exponents are all non-negative (zero or greater) integers.
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The degree of a polynomial function is…
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the largest exponent you see when the function is stated in descending powers form.
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A first degree polynomial function is…
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a linear function.
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A second degree polynomial function is …
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a quadratic (squartic) function.
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A third degree polynomial function is…
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a cubic function.
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A fourth degree polynomial function is…
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a quartic function.
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A fifth degree polynomial function is…
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a quintic function.
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Terms are…
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pieces of mathematical expressions that are added together.
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Factors are…
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pieces of mathematical expressions that are multiplied together.
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A monomial consists of…
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a coefficient, a variable, and an exponent.
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If the coefficient of a monomial is not showing then...
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it is a 1.
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If the exponent on the variable of a monomial is is not showing then...
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it is a 1.
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A monomial is…
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a polynomial with one term. (The degree may be anything.)
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A constant is...
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any real number as a term of a mathematical expression.
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True or false: A constant is a monomial.
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True. It can be thought of as a monomial of degree zero. That is, if there were a variable as a factor, then the exponent on that variable would be a zero. A constant is a monomial of degree zero.
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A binomial is…
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a polynomial with two terms. (The degree may be anything.)
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A trinomial is…
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a polynomial with three terms. (The degree may be anything.)
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End behavior of a polynomial function is determined by…
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the leading coefficient and the degree of the function.
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If the degree of a polynomial function is even, then the end behavior of the function is…
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a U-shape, opening up if the leading coefficient is positive and opening down if the leading coefficient is negative.
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If the degree of a polynomial function is odd, then the end behavior of the function is…
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down to the left and up to the right if the leading coefficient is positive, or up to the left and down to the right if the leading coefficient is negative.
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And end-behavior diagram consists of…
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two curved arrows, DISCONTINUOUS, that indicate the end behavior.
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The arrows in an end-behavior diagram are discontinuous because…
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except for linear equations and quadratics, what happens between end behaviors (hills and valleys) is unknown.
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Phrases that indicate direct variation are…
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‘y varies directly as x’ or ‘y is directly proportional to x’.
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Phrases that indicate inverse variation are…
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‘y varies inversely as x’ or ‘y is inversely proportional to x’.
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The phrases ‘y varies directly as x’ or ‘y is directly proportional to x’ translates to the mathematical equation…
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y = kx
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The phrases y varies inversely as x’ or ‘y is inversely proportional to x’ translates to the mathematical equation…
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y = k/x (but always write the fraction vertically).
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In a variation, the letter k represents…
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the constant of variation.
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Joint or combined variation means…
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more than one variable in addition to a constant of variation.
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The graph of a direct variation looks like…
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a line.
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The graph of an inverse variation looks like…
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two discontinuous L-shaped curves, for which both axes are asymptotes.
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An asymptote is…
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a line the curve approaches but does not touch. (Exceptions occur in rational functions.)
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Function arithmetic is…
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adding or subtracting or multiplying or dividing two functions.
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The notation f(x) + g(x) means…
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add the two functions together (simplify expressions where appropriate) to yield a third function.
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The notation f(x) + g(x) can also be written…
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(f + g)(x). The other arithmetical operations with functions are similar.
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The notation f(g(x)) means…
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a composition of functions. A value of the domain is processed through g(x), and then this new value is then processed through f(x).
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To write a composition of functions, such as f(g(x))…
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pick up the g function, and substitute it in ( ) wherever there is an x in the f function.
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The other notation for the composition of functions, such as f(g(x)) is…
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(fog)(x), a small circle beween f and g, not the letter ‘o’. It does NOT mean multiply.
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