Chapter 2: Linear Relations and Functions

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92 Terms

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Cartesian coordinate plane
________: composed of the x- axis (horizontal) and the y- axis (vertical), which meet at the origin (0, 0)
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Boundary
________: a line that shows the points that satisfy the inequality.
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Domain
________: a relation is the set of all first coordinates (x- coordinates) from the ordered pairs.
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Discrete
________: a relation in which the domain is a set of individual points.
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smooth curve
Continuous: a relation that can be graphed with a line or a(n) ________.
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Identity function
________: when the slope is 1, the x- values and y- values are equal.
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Linear equation
________: an equation that has no operations other than addition, subtraction, and multiplication of a variable by a constant.
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slope
If the line falls to the right, the ________ is negative.
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Scatter plot
________: a set of bivariate data graphed as ordered pairs in the coordinate plane.
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Piecewise
________: a function written using two or more expressions.
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vertical line
If no ________ intersects a graph in more than one point, the graph is a function.
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Constant function
________: when the slope is zero, every y- value is constant no matter what the x- value is.
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Rate of change
________: measures how much a quantity changes relative to the change in another quantity.
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Slope
________: the ratio of the change in y- coordinates to the corresponding change in x- coordinates.
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ordered pairs
data represented as an input and output, (x, y)
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Cartesian coordinate plane
composed of the x-axis (horizontal) and the y-axis (vertical), which meet at the origin (0, 0)
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relation
a set of ordered pairs
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domain
a relation is the set of all first coordinates (x-coordinates) from the ordered pairs
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range
the set of all second coordinates (y-coordinates) from the ordered pairs
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function
a special relation in which each domain value is paid with exactly **__ONE __**range value
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mapping
shows how the members are paired
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one-to-one function
a mapping in which each range value is paired with exactly ONE domain value
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discrete
a relation in which the domain is a set of individual points
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continuous
a relation that can be graphed with a line or a smooth curve
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vertical line test
how to test is a graph is a function
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independent variable
the variable whose values make up the domain (usually x)
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dependent variable
the variable whose values make up the range, the values that depend on the x (usually the y)
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linear equation
an equation that has no operations other than addition, subtraction, and multiplication of a variable by a constant
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linear function
a function whose ordered pairs satisfy a linear equation
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can be written in the form
f(x) = mx + b, where m and b are real numbers
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standard form
Ax + By = C, where A, B, and C are integers whose greatest common factor is 1
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y-intercept
the y-coordinate of the point where a graph crosses the y-axis
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x-intercept
the x-coordinate of the point where it crosses the x-axis
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rate of change
measures how much a quantity changes relative to the change in another quantity
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slope
the ratio of the change in y-coordinates to the corresponding change in x-coordinates
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family of graphs
a group of graphs that displays one or more similar characteristics
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parent graph
the simplest of the graphs in the family
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parallel lines
nonvertical lines with the same slope
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perpendicular lines
two lines are perpendicular if and ONLY if the product of their slopes is -1
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bivariate data
data with two variables
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scatter plot
a set of bivariate data graphed as ordered pairs in the coordinate plane
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positive correlation
positive slope in the scatter plot
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negative correlation
negative slope in the scatter plot
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no correlation
no visible trend, points are scattered and dont have a positive or negative direction
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line of fit
a line that approximates a set of data
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prediction equation
the equation for a line of fit
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step function
a function that is not linear, consists of line segments or rays
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greatest integer function
an example of a step function
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constant function
when the slope is zero, every y-value is constant no matter what the x-value is
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identity function
when the slope is 1, the x-values and y-values are equal
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absolute value function
f(x) = |x|
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piecewise
a function written using two or more expressions
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boundary
a line that shows the points that satisfy the inequality
54
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ordered pairs
data represented as an input and output, (x, y)
55
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Cartesian coordinate plane
composed of the x-axis (horizontal) and the y-axis (vertical), which meet at the origin (0, 0)
56
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relation
a set of ordered pairs
57
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domain
the set of all first coordinates (x-coordinates) from the ordered pairs
58
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range
the set of all second coordinates (y-coordinates) from the ordered pairs
59
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function
a special relation in which each domain value is paid with exactly ONE range value
60
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mapping
shows how the members are paired
61
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one-to-one function
a mapping in which each range value is paired with exactly ONE domain value
62
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discrete
a relation in which the domain is a set of individual points
63
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continuous
a relation that can be graphed with a line or a smooth curve
64
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vertical line test
how to test is a graph is a function
65
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independent variable
the variable whose values make up the domain (usually x)
66
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dependent variable
the variable whose values make up the range, the values that depend on the x (usually the y)
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linear equation
an equation that has no operations other than addition, subtraction, and multiplication of a variable by a constant
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linear function
a function whose ordered pairs satisfy a linear equation
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standard form
Ax + By = C, where A, B, and C are integers whose greatest common factor is 1
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y-intercept
the y-coordinate of the point where a graph crosses the y-axis
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x-intercept
the x-coordinate of the point where it crosses the x-axis
72
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rate of change
measures how much a quantity changes relative to the change in another quantity
73
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slope
the ratio of the change in y-coordinates to the corresponding change in x-coordinates
74
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family of graphs
a group of graphs that displays one or more similar characteristics
75
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parent graph
the simplest of the graphs in the family
76
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parallel lines
nonvertical lines with the same slope
77
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perpendicular lines
if and ONLY if the product of two lines' slopes is -1
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slope-intercept form
an equation written in the form: y = mx + b, where m is the slope and b is the y-intercept
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point-slope form
an equation written in the form: y - y1 = m(x - x1), where x1 and y1 are coordinates of a point on the line
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bivariate data
data with two variables
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scatter plot
a set of bivariate data graphed as ordered pairs in the coordinate plane
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positive correlation
positive slope in the scatter plot
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negative correlation
negative slope in the scatter plot
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no correlation
no visible trend, points are scattered and don’t have a positive or negative direction
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line of fit
a line that approximates a set of data
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prediction equation
the equation for a line of fit
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step function
a function that is not linear, consists of line segments or rays
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greatest integer function
an example of a step function, f(x) = [x]
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constant function
when the slope is zero, every y-value is constant no matter what the x-value is
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identity function
when the slope is 1, the x-values and y-values are equal
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piecewise
a function that is written using two or more expressions
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boundary
a line that shows the points that satisfy the inequality