Chapter 2: Linear Relations and Functions

Cartesian coordinate plane

: composed of the x- axis (horizontal) and the y- axis (vertical), which meet at the origin (0, 0)

Boundary

: a line that shows the points that satisfy the inequality.

Cartesian coordinate plane

: composed of the x- axis (horizontal) and the y- axis (vertical), which meet at the origin (0, 0)

Boundary

: a line that shows the points that satisfy the inequality.

Domain

: a relation is the set of all first coordinates (x- coordinates) from the ordered pairs.

Discrete

: a relation in which the domain is a set of individual points.

smooth curve

Continuous: a relation that can be graphed with a line or a(n) .

Identity function

: when the slope is 1, the x- values and y- values are equal.

Linear equation

: an equation that has no operations other than addition, subtraction, and multiplication of a variable by a constant.

slope

If the line falls to the right, the is negative.

Scatter plot

: a set of bivariate data graphed as ordered pairs in the coordinate plane.

Piecewise

: a function written using two or more expressions.

vertical line

If no intersects a graph in more than one point, the graph is a function.

Constant function

: when the slope is zero, every y- value is constant no matter what the x- value is.

Rate of change

: measures how much a quantity changes relative to the change in another quantity.

Slope

: the ratio of the change in y- coordinates to the corresponding change in x- coordinates.

ordered pairs

data represented as an input and output, (x, y)

Cartesian coordinate plane

composed of the x-axis (horizontal) and the y-axis (vertical), which meet at the origin (0, 0)

relation

a set of ordered pairs

domain

a relation is the set of all first coordinates (x-coordinates) from the ordered pairs

range

the set of all second coordinates (y-coordinates) from the ordered pairs

function

a special relation in which each domain value is paid with exactly __ONE __range value

mapping

shows how the members are paired

one-to-one function

a mapping in which each range value is paired with exactly ONE domain value

discrete

a relation in which the domain is a set of individual points

continuous

a relation that can be graphed with a line or a smooth curve

vertical line test

how to test is a graph is a function

independent variable

the variable whose values make up the domain (usually x)

dependent variable

the variable whose values make up the range, the values that depend on the x (usually the y)

linear equation

an equation that has no operations other than addition, subtraction, and multiplication of a variable by a constant

linear function

a function whose ordered pairs satisfy a linear equation

can be written in the form

f(x) = mx + b, where m and b are real numbers

standard form

Ax + By = C, where A, B, and C are integers whose greatest common factor is 1

y-intercept

the y-coordinate of the point where a graph crosses the y-axis

x-intercept

the x-coordinate of the point where it crosses the x-axis

rate of change

measures how much a quantity changes relative to the change in another quantity

slope

the ratio of the change in y-coordinates to the corresponding change in x-coordinates

family of graphs

a group of graphs that displays one or more similar characteristics

parent graph

the simplest of the graphs in the family

parallel lines

nonvertical lines with the same slope

perpendicular lines

two lines are perpendicular if and ONLY if the product of their slopes is -1

bivariate data

data with two variables

scatter plot

a set of bivariate data graphed as ordered pairs in the coordinate plane

positive correlation

positive slope in the scatter plot

negative correlation

negative slope in the scatter plot

no correlation

no visible trend, points are scattered and dont have a positive or negative direction

line of fit

a line that approximates a set of data

prediction equation

the equation for a line of fit

step function

a function that is not linear, consists of line segments or rays

greatest integer function

an example of a step function

constant function

when the slope is zero, every y-value is constant no matter what the x-value is

identity function

when the slope is 1, the x-values and y-values are equal

absolute value function

f(x) = |x|

piecewise

a function written using two or more expressions

boundary

a line that shows the points that satisfy the inequality

ordered pairs

data represented as an input and output, (x, y)

Cartesian coordinate plane

composed of the x-axis (horizontal) and the y-axis (vertical), which meet at the origin (0, 0)

relation

a set of ordered pairs

domain

the set of all first coordinates (x-coordinates) from the ordered pairs

range

the set of all second coordinates (y-coordinates) from the ordered pairs

function

a special relation in which each domain value is paid with exactly ONE range value

mapping

shows how the members are paired

one-to-one function

a mapping in which each range value is paired with exactly ONE domain value

discrete

a relation in which the domain is a set of individual points

continuous

a relation that can be graphed with a line or a smooth curve

vertical line test

how to test is a graph is a function

independent variable

the variable whose values make up the domain (usually x)

dependent variable

the variable whose values make up the range, the values that depend on the x (usually the y)

linear equation

an equation that has no operations other than addition, subtraction, and multiplication of a variable by a constant

linear function

a function whose ordered pairs satisfy a linear equation

standard form

Ax + By = C, where A, B, and C are integers whose greatest common factor is 1

y-intercept

the y-coordinate of the point where a graph crosses the y-axis

x-intercept

the x-coordinate of the point where it crosses the x-axis

rate of change

measures how much a quantity changes relative to the change in another quantity

slope

the ratio of the change in y-coordinates to the corresponding change in x-coordinates

family of graphs

a group of graphs that displays one or more similar characteristics

parent graph

the simplest of the graphs in the family

parallel lines

nonvertical lines with the same slope

perpendicular lines

if and ONLY if the product of two lines' slopes is -1

slope-intercept form

an equation written in the form: y = mx + b, where m is the slope and b is the y-intercept

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

bivariate data

data with two variables

scatter plot

a set of bivariate data graphed as ordered pairs in the coordinate plane

positive correlation

positive slope in the scatter plot

negative correlation

negative slope in the scatter plot

no correlation

no visible trend, points are scattered and don’t have a positive or negative direction

line of fit

a line that approximates a set of data

prediction equation

the equation for a line of fit

step function

a function that is not linear, consists of line segments or rays

greatest integer function

an example of a step function, f(x) = [x]

constant function

when the slope is zero, every y-value is constant no matter what the x-value is

identity function

when the slope is 1, the x-values and y-values are equal

piecewise

a function that is written using two or more expressions

boundary

a line that shows the points that satisfy the inequality