Lesson 4: Evaluating Types of Relations Flashcards
What are the four ways to express a relation according to the lesson?
Ordered Pairs, Table of Values, Mapping diagram, Graph
In ordered pairs, what are the domain and range of a relation?
The set for all first coordinates is the DOMAIN (x) of the relation. The set of all second coordinates is the RANGE 👍 of the relation.
What is shown in a Table of Values representing a relation?
X -5 -7 5 7
Y 3 4 3 4
How is a mapping diagram used to show a relation?
X -5 -7 5 7
Y 3 4 3 4
What simplified mapping diagram example was shown in the lesson?
X -5 -7 5 7
Y 3 4
What are the three types of relation discussed?
One-to-one, One-to-many, Many-to-one
What is an example of a One-to-one relation using a table of values?
X 1 2 3 4 5
Y 1 3 5 7 9
What is an example of a One-to-many relation?
X 1 3
Y 1 3 5 7 9
What is an example of a Many-to-one relation?
X 1 2 3 4 5
Y 3 5 9
What is a function in terms of x and y values?
In a function, the value of y depends on the value of x. Because the value of y is dependent on the value of x, y is called the dependent variable, whereas x is called the independent variable.
__ is dependent on the value of _
y is dependent on the value of x
__ is called the dependent variable, whereas _ is called the independent variable.
y is called the dependent variable, whereas x is called the independent variable.
How is y determined in a function given f(x)?
The value of y can be determined by evaluating f(x) based on the value of x.
How can we identify whether a given relation is a function or not?
By using the Vertical Line Test
What is the Vertical Line Test and how is it used?
A simple way to test whether a graph is a function is using the vertical line test. This is done by positioning a straightedge over any part of the graph parallel to the y-axis and moving it about both ends of the x-axis. If the straightedge intersects the graph at only one point as it is moved, then the graph indicates a function.
What does it mean when a graph passes the Vertical Line Test?
It means the graph is a function. Note: The vertical should only hit the graph once.
What does it mean when a graph fails the Vertical Line Test?
It is not a function.
What type of relation is shown if there is repetition in y-values for different x-values?
Many-to-one
What type of relation is shown if there is no repetition of values and each x maps to a unique y?
One-to-one
What type of relation is shown if one x-value maps to multiple y-values?
One-to-many
True or False: All functions are relations.
True
True or False: All relations are functions.
False
True or False: If two points in a set of ordered pairs have the same x-coordinates, the relation is not a function.
True
True or False: A many-to-many correspondence is not a function.
True
True or False: The association between a student and his ID number is a function.
True
