1. A relationship from one set (called the domain) to another set (called the range) that assigns to each element of the domain exactly one element of the range. 2. The action or actions that an item is designed to perform.
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increasing function
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A graph that has a positive slope and shows growth
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extrema
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The maximum and minimum values of a function.
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equation
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A mathematical sentence that contains an equal sign
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term
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A number, a variable, or the product of a number and a variable
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x coordinate
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1st number of an ordered pair
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y axes
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on a coordinate what is always the second number?
vertical placement
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order of operations
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the order in which operations in an expression to be evaluated are carried out. 1. parentheses 2. exponets 3. multiplication and divison 4. addition and subtraction
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nonlinear function
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is a function whose graph is not a line or part of a line.
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decreasing function
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A graph that has a negative slope and shows decay
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simplest form
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an expression that contains no like terms or parenthesis
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relation
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A set of ordered pairs
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origin
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the point where the axes intersect
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coefficient
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A number multiplied by a variable in an algebraic expression.
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reciprocal
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The multiplicative inverse
One of a pair of numbers whose product is 1: the reciprocal of 2/3 is 3/2
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negative function
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On a graph Lies below the x-axis
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set
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collection of objects or numbers that is shown using brackets
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x axes
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on a coordinate what is always the first number?
horizontal placement
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relative maximum
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A point on the graph of a function where no other nearby points have a greater y-coordinate.
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line of symmetry
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an imaginary line that divides an image into two halves, thereby causing one half to be the reflection of the other
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multiplicative identity
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5 x 1 = 5
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function notation
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use the symbol f(x) in place of y
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domain
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Set of all x-values, (independent)
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dependent variable
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y values, range, depends on another value
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independent variable
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x values, domain
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continuous function
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A function whose graph is an unbroken line or smooth curve with no gaps or breaks.
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positive function
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On graph lies above x- axis
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coordinate plane
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A coordinate system formed by the intersection of a horizontal number line, called the x-axis, and a vertical number line, called the y-axis.
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multiplicative inverse
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The reciprocal
One of a pair of numbers whose product is 1: the reciprocal of 2/3 is 3/2
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ordered pair
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a pair of numbers used to locate a point on the coordinate plane.
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additive identity
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a + 0 = a
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like terms
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Expressions that contain the same variables to the same power
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evaluate
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Finding the value of an expression
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variable
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A symbol used to represent a quantity that can change
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equivalent expression
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Expressions that have the same value.
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solution
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a number that makes an equation true
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element
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each object or number in a set
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y-intercept
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The point where the graph crosses the y-axis
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algebraic expression
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A mathematical phrase involving at least one variable and sometimes numbers and operation symbols.
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y coordinate
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2nd number of an ordered pair.
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identity
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an equation that is true for every value of the variable
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mapping
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Illustrates how each element of the domain is paired with an element in the range.
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x-intercept
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The point where the graph crosses the x-axis
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end behavior
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The behavior of the graph as x approaches positive infinity or negative infinity.
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power
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exponent value
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relative minimum
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A point on the graph of a function where no other nearby points have a lesser y-coordinate.
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vertical line test
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If any vertical line passes through more than one point of the graph, then the relation is not a function
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intercept
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where a graph crosses an x or y axis
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coordinate system
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A graph with a horizontal number line (x-axis) and a vertical number line (y-axis) that are perpendicular to each other. The point of intersection is called the origin and labeled 0 on the graph. An ordered pair (x,y) is used to name a point on a coordinate system.