Relations and Functions

The video tutorial explains the concept of functions, distinguishing them from general relations. It covers various methods to determine if a relation is a function, including ordered pairs, tabular data, algebraic rules, arrow diagrams, and graphical representation using the vertical line test. Examples are provided to illustrate each method, emphasizing the importance of unique mappings from domain to range.

What is a necessary condition for a relation to be considered a function when using ordered pairs?

• The second element must be unique.

• The first element must not repeat.

• The sum of elements must be even.

• The first element must be greater than the second.

In a tabular representation, what indicates that a relation is not a function?

• The first column has unique values.

• The second column has repeated values.

• The first column has repeated values.

• The second column has unique values.

What must be true for a relation defined by an algebraic rule to be a function?

• Distinct values of X must yield distinct function values.

• Distinct values of X must yield the same function value.

• The function must be linear.

• The function must be quadratic.

Why is the relation F(x) = √x not considered a function?

• It has no image for negative numbers.

• It has multiple images for positive numbers.

• It is not defined for real numbers.

• It is not continuous.

What is the first step in determining if a relation in an arrow diagram is a function?

• Check if each element in the first set has multiple images.

• Check if the second set is completely used up.

• Check if the first set is completely used up.

• Check if each element in the second set has one image.

What does the vertical line test determine about a graph?

• If the graph is decreasing.

• If the graph is increasing.

• If the graph is a function.

• If the graph is continuous.

Why does a circle fail the vertical line test?

• It has no center.

• It is not symmetric.

• It is not a closed shape.

• It intersects the vertical line more than once.