Chapter 2: Linear Relations and Functions

0.0(0)
linked notesView linked note
learnLearn
examPractice Test
spaced repetitionSpaced Repetition
heart puzzleMatch
flashcardsFlashcards
Card Sorting

1/91

encourage image

There's no tags or description

Looks like no tags are added yet.

Study Analytics
Name
Mastery
Learn
Test
Matching
Spaced

No study sessions yet.

92 Terms

1
New cards
Cartesian coordinate plane
________: composed of the x- axis (horizontal) and the y- axis (vertical), which meet at the origin (0, 0)
2
New cards
Boundary
________: a line that shows the points that satisfy the inequality.
3
New cards
Domain
________: a relation is the set of all first coordinates (x- coordinates) from the ordered pairs.
4
New cards
Discrete
________: a relation in which the domain is a set of individual points.
5
New cards
smooth curve
Continuous: a relation that can be graphed with a line or a(n) ________.
6
New cards
Identity function
________: when the slope is 1, the x- values and y- values are equal.
7
New cards
Linear equation
________: an equation that has no operations other than addition, subtraction, and multiplication of a variable by a constant.
8
New cards
slope
If the line falls to the right, the ________ is negative.
9
New cards
Scatter plot
________: a set of bivariate data graphed as ordered pairs in the coordinate plane.
10
New cards
Piecewise
________: a function written using two or more expressions.
11
New cards
vertical line
If no ________ intersects a graph in more than one point, the graph is a function.
12
New cards
Constant function
________: when the slope is zero, every y- value is constant no matter what the x- value is.
13
New cards
Rate of change
________: measures how much a quantity changes relative to the change in another quantity.
14
New cards
Slope
________: the ratio of the change in y- coordinates to the corresponding change in x- coordinates.
15
New cards
ordered pairs
data represented as an input and output, (x, y)
16
New cards
Cartesian coordinate plane
composed of the x-axis (horizontal) and the y-axis (vertical), which meet at the origin (0, 0)
17
New cards
relation
a set of ordered pairs
18
New cards
domain
a relation is the set of all first coordinates (x-coordinates) from the ordered pairs
19
New cards
range
the set of all second coordinates (y-coordinates) from the ordered pairs
20
New cards
function
a special relation in which each domain value is paid with exactly **__ONE __**range value
21
New cards
mapping
shows how the members are paired
22
New cards
one-to-one function
a mapping in which each range value is paired with exactly ONE domain value
23
New cards
discrete
a relation in which the domain is a set of individual points
24
New cards
continuous
a relation that can be graphed with a line or a smooth curve
25
New cards
vertical line test
how to test is a graph is a function
26
New cards
independent variable
the variable whose values make up the domain (usually x)
27
New cards
dependent variable
the variable whose values make up the range, the values that depend on the x (usually the y)
28
New cards
linear equation
an equation that has no operations other than addition, subtraction, and multiplication of a variable by a constant
29
New cards
linear function
a function whose ordered pairs satisfy a linear equation
30
New cards
can be written in the form
f(x) = mx + b, where m and b are real numbers
31
New cards
standard form
Ax + By = C, where A, B, and C are integers whose greatest common factor is 1
32
New cards
y-intercept
the y-coordinate of the point where a graph crosses the y-axis
33
New cards
x-intercept
the x-coordinate of the point where it crosses the x-axis
34
New cards
rate of change
measures how much a quantity changes relative to the change in another quantity
35
New cards
slope
the ratio of the change in y-coordinates to the corresponding change in x-coordinates
36
New cards
family of graphs
a group of graphs that displays one or more similar characteristics
37
New cards
parent graph
the simplest of the graphs in the family
38
New cards
parallel lines
nonvertical lines with the same slope
39
New cards
perpendicular lines
two lines are perpendicular if and ONLY if the product of their slopes is -1
40
New cards
bivariate data
data with two variables
41
New cards
scatter plot
a set of bivariate data graphed as ordered pairs in the coordinate plane
42
New cards
positive correlation
positive slope in the scatter plot
43
New cards
negative correlation
negative slope in the scatter plot
44
New cards
no correlation
no visible trend, points are scattered and dont have a positive or negative direction
45
New cards
line of fit
a line that approximates a set of data
46
New cards
prediction equation
the equation for a line of fit
47
New cards
step function
a function that is not linear, consists of line segments or rays
48
New cards
greatest integer function
an example of a step function
49
New cards
constant function
when the slope is zero, every y-value is constant no matter what the x-value is
50
New cards
identity function
when the slope is 1, the x-values and y-values are equal
51
New cards
absolute value function
f(x) = |x|
52
New cards
piecewise
a function written using two or more expressions
53
New cards
boundary
a line that shows the points that satisfy the inequality
54
New cards
ordered pairs
data represented as an input and output, (x, y)
55
New cards
Cartesian coordinate plane
composed of the x-axis (horizontal) and the y-axis (vertical), which meet at the origin (0, 0)
56
New cards
relation
a set of ordered pairs
57
New cards
domain
the set of all first coordinates (x-coordinates) from the ordered pairs
58
New cards
range
the set of all second coordinates (y-coordinates) from the ordered pairs
59
New cards
function
a special relation in which each domain value is paid with exactly ONE range value
60
New cards
mapping
shows how the members are paired
61
New cards
one-to-one function
a mapping in which each range value is paired with exactly ONE domain value
62
New cards
discrete
a relation in which the domain is a set of individual points
63
New cards
continuous
a relation that can be graphed with a line or a smooth curve
64
New cards
vertical line test
how to test is a graph is a function
65
New cards
independent variable
the variable whose values make up the domain (usually x)
66
New cards
dependent variable
the variable whose values make up the range, the values that depend on the x (usually the y)
67
New cards
linear equation
an equation that has no operations other than addition, subtraction, and multiplication of a variable by a constant
68
New cards
linear function
a function whose ordered pairs satisfy a linear equation
69
New cards
standard form
Ax + By = C, where A, B, and C are integers whose greatest common factor is 1
70
New cards
y-intercept
the y-coordinate of the point where a graph crosses the y-axis
71
New cards
x-intercept
the x-coordinate of the point where it crosses the x-axis
72
New cards
rate of change
measures how much a quantity changes relative to the change in another quantity
73
New cards
slope
the ratio of the change in y-coordinates to the corresponding change in x-coordinates
74
New cards
family of graphs
a group of graphs that displays one or more similar characteristics
75
New cards
parent graph
the simplest of the graphs in the family
76
New cards
parallel lines
nonvertical lines with the same slope
77
New cards
perpendicular lines
if and ONLY if the product of two lines' slopes is -1
78
New cards
slope-intercept form
an equation written in the form: y = mx + b, where m is the slope and b is the y-intercept
79
New cards
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
80
New cards
bivariate data
data with two variables
81
New cards
scatter plot
a set of bivariate data graphed as ordered pairs in the coordinate plane
82
New cards
positive correlation
positive slope in the scatter plot
83
New cards
negative correlation
negative slope in the scatter plot
84
New cards
no correlation
no visible trend, points are scattered and don’t have a positive or negative direction
85
New cards
line of fit
a line that approximates a set of data
86
New cards
prediction equation
the equation for a line of fit
87
New cards
step function
a function that is not linear, consists of line segments or rays
88
New cards
greatest integer function
an example of a step function, f(x) = [x]
89
New cards
constant function
when the slope is zero, every y-value is constant no matter what the x-value is
90
New cards
identity function
when the slope is 1, the x-values and y-values are equal
91
New cards
piecewise
a function that is written using two or more expressions
92
New cards
boundary
a line that shows the points that satisfy the inequality