Lesson 6: representing relations
Words to Know
Coordinate System: the system we use to graph - formed by two number lines, the horizontal and vertical
x-axis: the horizontal axis in the coordinate system
y-axis: the vertical axis in the coordinate system
ordered pair: the set of numbers, or coordinates: (x, y)
x-coordinate: the x-value, represents the horizontal placement of the point
y-coordinate: the y-value, represents the vertical placement of the point
Origin: (0,0), the point where the axes intersect
Relation: a set of ordered pairs, they can be represented in a table, graphed or mapped
Mapping: illustrates how each element of the domain (x-values) is paired with each element in the range (y-values).
Independent Variable: the variable that determines the output (graphed on the x-axis)
Dependent Variable: the variable with a value that is dependent on the independent variable (graphed on the y-axis.
x-axis: the horizontal axis in the coordinate system
y-axis: the vertical axis in the coordinate system
ordered pair: the set of numbers, or coordinates: (x, y)
x-coordinate: the x-value, represents the horizontal placement of the point
y-coordinate: the y-value, represents the vertical placement of the point
Origin: (0,0), the point where the axes intersect
Relation: a set of ordered pairs, they can be represented in a table, graphed or mapped
Mapping: illustrates how each element of the domain (x-values) is paired with each element in the range (y-values).
Independent Variable: the variable that determines the output (graphed on the x-axis)
Dependent Variable: the variable with a value that is dependent on the independent variable (graphed on the y-axis.
Examples
1. Representations of a Relation
Express {(4, -3), (3, 2), (-4, 1), (0, -3) as a table, graph, and mapping. State the domain and range.
Domain: {4, 3, -4, 0}
Range: {-3, 2, 1, -3}
Express {(4, -3), (3, 2), (-4, 1), (0, -3) as a table, graph, and mapping. State the domain and range.
Domain: {4, 3, -4, 0}
Range: {-3, 2, 1, -3}
2. Independent and Dependent Variables
State the independent and dependent variables for each relation:
a) The air pressure inside a tire increases with the temperature.
I: Temperature
D: Air pressure
b) As the amount of rain decreases, so does the water level of the river
I: Amount of rain
D: water level
c) The more tickets the dance committee sells for the spring dance, the greater amount of money they can spend on their trip.
I: tickets
D: money
State the independent and dependent variables for each relation:
a) The air pressure inside a tire increases with the temperature.
I: Temperature
D: Air pressure
b) As the amount of rain decreases, so does the water level of the river
I: Amount of rain
D: water level
c) The more tickets the dance committee sells for the spring dance, the greater amount of money they can spend on their trip.
I: tickets
D: money
3. Analyze Graphs
Describe what is happening in each graph:
a)
Describe what is happening in each graph:
a)
b)
Tips
When mapping, the arrow goes from the x to the y.
The independent variable is the one that is constant, for example: time.
The independent variable is the one that is constant, for example: time.
Extra Examples
Click here for additional examples and self check quizzes
Problems of the Day
1. Identify the independent and dependent variables: The number of calories you burn increases as the number of minutes that you walk increases.
2. Analyze the following graph:
2. Analyze the following graph: